That's the view of the Mail on Sunday's Martin Samuel who believes that former Chelsea boss Mourinho would relish the chance of winning the Premier League title at Anfield.
The Portuguese has the backing of England and United defender Rio Ferdinand who told GQ magazine Mourinho has the "ego and personality" to succeed Sir Alex Ferguson once the Scot's long-term tenure comes to an end.
And Samuel agreed, in part, saying on The Supplement: "Whoever is going to replace Alex has got to have a very strong personality.
"He's got to be the sort of guy who thinks he can go in there and do better and it's going to be extraordinarily hard for anyone to do better than Sir Alex Ferguson.
"But if there is anyone who fancies himself enough to think 'I can take this on, they will be a better team under me', it is Jose.
"I think he would like to come back to England. Liverpool would suit him more, I think, because there will be that little bit of one-upmanship with (Rafa) Benitez. He will be very, very aware that they haven't won the league in so long.
"That would appeal to Jose - to go there and actually go there and be the guy who brings the title back to Anfield - so I think that might appeal to him more than Manchester United but he can do either job."
UniqueGiven Ferguson's success at United, Samuel felt that whoever does take over from the Scot might only be in the position for one or two seasons.
"Maybe after Ferguson, for a short period of time, they don't actually need a team-builder. What you need is someone who is going to take the team on for a short period of time and that makes the break with Ferguson," he said.
"That for two years might be worth more than getting someone to try and continue what Sir Alex has done because it's such a unique job what he's done."
Neil Custis, of The Sun, believes Ferguson has no intention of going anywhere soon but says Mourinho appears to think he is the right man to fill the Old Trafford hot-seat when it does become vacant.
"I think he (Ferguson) will be around for another couple of years at least. I don't see any change in his drive and determination," Custis said.
"Jose has played a very good political game in that he's stayed very close to Fergie. When he comes to Old Trafford now - which he does whenever he possibly can to watch a game - he walks around as if he is the manager!
"The entrance down the tunnel to go onto the pitch is only the opposition and the home players that go in there. He walks in that entrance and wanders around and just goes where he wants!
"Before one game he went and sat in the Directors' box on his own half-an-hour before the match and he was just staring around the stadium taking it all in and you just thought 'he's thinking I would really, really fancy this'."