The Red Devils could be forgiven for wanting to put their feet up for the rest of the month, basking in the glow of pulling off one of the biggest transfer coups in recent seasons by beating Manchester City to the signing of Sánchez, and looking ahead to what the Portuguese boss has in store with his future now tied to Old Trafford until at least 2020.
But reports suggest United might not be finished yet; it is claimed the 20-time champions of England could look to make one further addition before the mid-season transfer window closes on January 31.
Club captain Michael Carrick, who has been out of action lately due to a heart condition, has announced his plans to retire at the end of the current campaign, while, as things stand, Marouane Fellaini will be a free agent come summer, having been unable to come to terms on a contract renewal.
Already a little light in the central midfield area, the losses of Carrick and Fellaini could leave United stretched. Plus, it is widely believed Mourinho must revert to a 4-3-3 formation in order to get the best out of record signing Paul Pogba, which might require at least one new recruit before becoming plausible.
The most likely outcome remains that United will keep their powder dry from now until summer, when a wider range of suitable midfield candidates will be available to them; it would be near impossible to acquire a player of reported target Sergej Milinković-Savić's stature this month, for instance.
But if Mourinho can't wait into the end of the season, here are four central midfielders he could realistically target before the end of January.
Jean Michaël Seri – Nice
Linked with Barcelona and Paris Saint-Germain last summer, few would've expected Seri to still be a Nice player by the start of 2017/18. But no such move materialised for the 26-year-old Ivory Coast international, who is now attracting interest from both United an Manchester City, according to The Mirror.
At 5ft 5ins, Seri doesn't fit the mould of the powerful, athletic midfielders Mourinho has gone for in recent years, but he has all the technical quality to thrive at Old Trafford.
Signed from Paços de Ferreira as a defensive midfielder in 2015, Nice soon realised the diminutive playmaker had too much to offer going forward to be confined to the role of a destroyer, giving him the licence to roam into the opposition's half from his deep starting position.
Although not an outstanding ball-winner, averaging one tackle and 0.8 interceptions per 90 this season, Seri is an exceptional conductor of play, making an incredible 96.2 passes per 90 – more than any United player – at a completion rate of 90.6 per cent.
Capable of splitting defences with incisive forward passes, Seri returned nine Ligue 1 assists last season – as well as chipping in with seven goals – and is averaging more key passes per 90 (2.6) than any current United player this term. Valued at around £30million, the Nice star would be a snip in the current market.
Mateo Kovačić – Real Madrid
Since signing for Real Madrid from Inter Milan in a £30million deal in 2015, Kovačić has won the Champions League twice and earned a La Liga winners' medal last season.
But the Croatian cannot be satisfied with his role at the Bernabéu. In three-and-a-half seasons with Los Blancos, he has started only 28 league games, with just one of those coming this term.
There has never been any doubt over the 23-year-old's talent; he is positionally responsible, passes well with either foot and is creative in the final third. But, with Luka Modrić, Toni Kroos, Casemiro and Isco ahead of him in the pecking order, Kovačić is unlikely to ever receive a satisfactory amount of game time in the Spanish capital.
Previously linked with Liverpool, some reports suggest Madrid will offer Kovačić, along with goalkeeper Keylor Navas, in a player(s)-plus-cash deal for David de Gea in the summer. United should steer well clear of any such bid, as their No.1 is too important to part ways with.
But this does seem to indicate that Madrid view Kovačić as expendable, something United could take advantage of this month.
Fred – Shakhtar Donetsk
Thought to be at the centre of a transfer tussle between United and City, Shakhtar midfielder Fred has impressed in the Champions League this season, helping the Ukrainian champions progress to the knockout rounds at the expense of Serie A leaders Napoli.
A dynamic presence in the middle third, the energetic 24-year-old has demonstrated excellent ball-recovery skills in Europe's premier club competition this term, making 1.2 interceptions and 2.7 tackles per 90, as well as showcasing his samba flair with 20 completed dribbles from 21 attempts.
Muscular and defensively aware, Fred could help Nemanja Matić in freeing up Pogba in the United midfield, while his ability to drive forward and link with wide runners would help ease the creative and ball-progression burdens the Frenchman is currently forced to bear at Old Trafford.
City are believed to be in the driver's seat when it comes to the two clubs' respective chances of landing the Brazil international, but United have already trumped their rivals once in the transfer market this month.
Radja Nainggolan – Roma
Just a few weeks ago it would have seemed almost impossible to prise a player of Nainggolan's quality and importance away from Roma as they battle to secure a place in next season's Champions League.
But recent indiscretions have caused the Belgian midfielder's status at the Olympic Stadium to become a little more uncertain. The 29-year-old box-to-box powerhouse was reprimanded recently and forced to publicly apologise for posting an Instagram video in which he could be seen smoking and drinking on New Year's Eve.
In the immediate aftermath, Nainggolan, who has never made any secret of being a smoker, was linked with a £40million move to the Chinese Super League.
Having issued his apology, the dust seems to have settled and it remains likely he will stay with Roma for the rest of the season. But, linked with both United and Chelsea in the past, the Red Devils might be wise to test the water with a January bid for the the former Cagliari midfielder.
Last season, Nainggolan produced the best form of his career for Roma, returning 11 goals and five assists. While he hasn't quite hit the same heights this term, his experience, technical quality and drive could be the perfect counterbalance to Pogba in a midfield three.