After joining the club as a youth player from Gillingham, he made just 26 league appearances before being allowed to leave by the Portuguese manager.
Since his move to Southampton, first on loan and then for a reported £10million fee, Bertrand has proved himself as one of the best left-backs in England.
He has made more than 100 appearances for the Saints, was named in the PFA Premier League Team of the Year for 2014/15 and was part of England’s Euro 2016 squad.
Like Romelu Lukaku, it isn't hard to imagine him being first choice at Stamford Bridge now had Mourinho moved him on.
If he does arrive at the Etihad Stadium, he would be the second player to play for City – after Kevin de Bruyne – who had been shunned by Mourinho at Chelsea.
Why would City want Bertrand?
Kyle Walker and Benjamin Mendy joined along with Real Madrid's Danilo. But Mendy, who had made a fine start since his switch from Monaco has been ruled out for the season after suffering knee ligament damage.
Guardiola ended last season with four at the back, but was known to dabble with three at the back and has done so again in the early weeks of this season.
And while you would predominantly expect Bertrand to play as a left-back, if City were to use three at the back, he could play very easily as a left-sided centre-back, a role which he played for Southampton under Ronald Koeman.
“I’m enjoying it, to be honest,” he said last year when asked about how he felt playing in that position.
“You're more of a centre-back first and foremost and your natural ability in that position is an added bonus, because we do have quite a lot of possession between the back three, and it's important that the back three do pick the right passes and get us on our way.”
César Azpilicueta has shown that natural full-backs can play the role either side of a back three and thrive, so there’s no reason Bertrand shouldn’t either, should Guardiola ask him to play there.
How does he compare to Mendy?
In the first few weeks since his move from Monaco, Mendy has set the standard for Premier League full-backs with his direct running, delivery and solidity. But his season is all but over and Fabian Delph has had to fill in in lieu of a natural left-back.
We have had a look at the 2016/17 league statistics for Bertrand and Mendy to see how they compare.
There is no way of disguising the fact Mendy comes out on top in all but one metric.
Bertrand has more shots per 90 minutes, 0.68 to 0.61, with a higher accuracy, 46 per cent to 36 per cent, but that’s about all that looks good for him compared to the Monaco man.
The French international comes out on top in terms of chances created per 90 minutes – 1.09 to 0.61.
He also has more successful take ons per 90 minutes too – 1.62 to just 0.54 – and in terms of attempted take ons, Mendy has a better rate of pulling them off, completing 56.06 per cent of his to just 38.46 per cent when it comes to Bertrand.
Per 90 minutes, he also wins more tackles (1.75 to 0.93), more interceptions (1.84 to 1.69) and makes more clearances too (3.32 to 2.3).
But you have to take into account that Monaco are a much more attacking team than Southampton, and they both play in very different leagues.
But perhaps Monaco’s style is more similar to that of Guardiola at City – the two sides did produce a goalscoring bonanza when they met in the Champions League this season. That may give Mendy the advantage, as would the fact he is five years Bertrand's junior at just 22.
This is probably Bertrand’s last chance to prove himself at a Champions League club, though, and it’s hard to say that he does not deserve to get that opportunity after his impressive work at Southampton.
If he does sign, he may not be the biggest name to come through the door, but his intelligence may make him into one of the most vital in Guardiola’s style of play, where his full-backs are so crucial.