That was until Manchester United swooped, with the Red Devils now reportedly on the brink of sealing a £75million deal for the striker.
The Daily Mail and the BBC were first to report United had seen a bid accepted for the powerful Belgian striker and there are claims the 24-year-old will undergo a medical in Los Angeles — where his is currently holidaying with Paul Pogba — ahead of joining up with his new team-mates for their pre-season US tour.
Having supposedly been close to clinching a deal to sign Álvaro Morata — who is now a Chelsea transfer target — from Real Madrid, United quickly shifted gears when it became apparent the Blues' move for Lukaku had stalled.
It allowed Mourinho the opportunity to snare a striker who had apparently topped his wish-list all along — despite the fact that he was the one who sold the player to Everton during his Stamford Bridge reign.
With all but the formalities to be completed, Lukaku represents a stellar addition for United, and here are the five ways he will improve the Old Trafford club's attack.
United didn't lack for creativity last term, ranking fourth in the Premier League for chances created (447) in 2016/17, behind only Tottenham Hotspur (504), Liverpool (496) and Manchester City (482).
But putting those chances away was a major issue, with Mourinho's side eighth when it came to goals scored (54) – behind even Bournemouth (55).
More damning still is that United’s conversion rate of 13 percent ranked them 17th in the English top fight, ahead of only Sunderland (11.6 per cent), Middlesbrough (11.3 per cent) and Southampton (10.7 per cent).
By way of comparison, league leaders Chelsea scored 20.9 per cent of their shots last season, and the average conversion rate for the division was 15.6 per cent.
Zlatan Ibrahimović, who has since departed the club, led the line for the Red Devils, scoring an impressive 28 goals in all competition after many observers had tipped the 35-year-old to flop upon his arrival in England.
With 17 league strikes, he was United‘s highest scorer by far, with Juan Mata's six goals making the Spaniard a distant second.
However, it was Mata who proved to be the side's most reliable finisher, converting 15 per cent of his 40 shots, while Ibrahimović's conversion rate was 14.78 per cent.
Neither of these averages are especially impressive, with an elite marksman typically finishing at least 20 per cent of his shots at goal. Lukaku, who bagged an impressive 25 goals for Everton last term, netted 22.72 per cent of his efforts.
The kind of clinical touch the Belgian has demonstrated in his time at Goodison Park would be an enormous boon to United, who would likely have fared better than their sixth-place finish had they been a little more ruthless in front of goal.
What's more, Lukaku, despite being pipped to the Premier League Golden Boot by Harry Kane, returned 24 non-penalty goals in 2016/17, a figure that no player in the division could beat.
Although predominantly left-footed, Lukaku is a threat from anywhere inside the penalty area on his weaker right side, and, standing at 6ft 3ins, is also a powerful aerial threat.
Of his 25 league goals last season, 12 were scored with his left foot, seven with his right, and six were headers — a remarkably impressive spread.
No United player found the net more than twice with their weaker foot in the Premier League last season, nor could any match his return of six headers.
This goes to show that, upon his anticipated arrival at Old Trafford, the Belgian, who is vastly experienced for one so young, will pose a much more well-rounded goal threat than anyone currently at Mourinho's disposal.
Although he is not a target man as such – and much more suitably suits the characterisation of a penalty-box poacher than the kind of player who looks to bring the ball down and link play – the Everton man fits the bill for the kind of physical presence Mourinho has always had leading the line in his great sides of the past.
Athletic and agile, yet strong and imposing, on his day Lukaku is unplayable and possesses many of the attributes that made Didier Drogba — with whom Mourinho won three Premier League titles at Chelsea — such a dominant force.
Lukaku is often labelled as a flat-track bully for a perceived inability to produce the goods against top teams.
This is somewhat of a misconception, as only four players could top the Everton striker's return of four goals against the Premier League's top six sides last season. He also managed to plunder a hat-trick against his prospective new employers for West Bromwich Albion in Sir Alex Ferguson's last game as United boss in 2013.
Part of the reason some may feel Lukaku is less able to impact games against high-calibre opponents is an issue of perception.
Due to his size an physical presence, people expect the Belgian to be the kind of striker through whom all of his team's moves are filtered, dropping off the frontline, bringing the ball under control and linking with midfield runners. But that's not his game – again, he's a poacher rather than a target man.
As such, Lukaku is only as effective as the service he receives. Playing in an upper-mid-table side such as Everton, it stands to reason that he is not supplied with as much ammunition against the higher-ranked sides.
Give him chances and he will score. Against anyone.
Besides, one of United's major failings last season was that they struggled to kill off inferior opponents, squandering chance after chance, failing to turn one point into three in home games against the likes of West Brom, Stoke City and Burnley among others.
No team in the Premier League missed more “big chances” than United last term (50), with no player squandering more of those opportunities than Ibrahimović (17).
Contrastingly, Lukaku scored more big chances (17) than any other player in the division. And with 80 of his 85 total Premier League goals (94.12 per cent) coming from inside the penalty area, he is exactly the kind of “fox in the box” Mourinho's side is crying out for.
For all his goals and the winning mentality he restored upon swaggering through the Old Trafford door, one of the main criticisms of Ibrahimović, aside from his inconsistent finishing, was his lack of mobility at the point of the attack.
At 35, it is to be expected that the former Barcelona and Ajax star is not perhaps as quick as he once was, although he was never blessed with anything resembling true pace.
Ibrahimović was much more comfortable dropping into the No.10 space between the opposition's defence and midfield to receive the ball to feet, rather than playing on the shoulder of the last defender and looking to burst in behind the backline.
When he did saunter beyond the ball into the penalty area, he would typically pull towards the back post and invite a lofted ball to contest aerially.
This all meant United's attack would often be too predictable, slowing down in the final third and playing into the hands of side's who came to Old Trafford to sit deep and defend the edge of their 18-yard box.
With Lukaku, there would be no such issue. The former Chelsea man is tremendously quick over short distances and times his runs very well.
His presence as the spearhead of United's attack would stretch the pitch, force the opposition to worry about a threat in behind rather than simply dealing with everything in front.
With the likes of Anthony Martial, Marcus Rashford and Henrikh Mkhitaryan flanking him, Lukaku's speed could see the Red Devils become a real counter-attacking threat too.
Helping Pogba Shine
One of the key advantages that Lukaku could bring to Old Trafford, and one that as yet isn't really being discussed, is the impact he could have on Pogba.
The French superstar was United's marquee signing of last summer, returning to the club from Juventus for a world-record £89million fee.
Despite many overly-critical appraisals of his performances, the 24-year-old stood-out as easily the side's most gifted player, but his numbers were below what was expected, with his return of five Premier League assists a particular bone of contention for some.
However, Pogba was a regular chance creator last term, making two key passes per 90 minutes. He was also often the man to unlock a stubborn defence, only for his efforts to be rendered futile by poor finishing.
Not only will Lukaku offer a more clinical target for Pogba's passes, he will also be a more readily available one thanks to his movement and propensity for bursting in behind the opposition.
The advantage of having such a player is two-fold for Pogba. Lukaku's pace and movement provides passing options but also forces the opponent's defence to drop back, creating space in the kind of central attacking zones from where the Frenchman's creative gifts are of most use to United.