Manchester United have shelled out over £100million as they aim to win the title for the first time since 2013, when Sir Alex Ferguson was in charge.
David Moyes and Louis van Gaal both failed to mount challenges for the country’s biggest prize and were sacked after failing to do so.
Jose Mourinho took the reins last summer and, though United finished sixth during his maiden season at the helm, trophy triumphs in the form of the EFL Cup and Europa League saved him from the axe.
Victor Lindelof, Romelu Lukaku and Nemanja Matic have all been brought in.
But though Carragher thinks United may make a fight of things this season, the Liverpool legend thinks Chelsea and Manchester City will finish above them.
“I don’t think they will win the league,” he told Sky Sports.
“But they will have a real title challenge.
“I see the title being between Man City and Chelsea, personally.”
United continue to be linked with wingers ahead of the end of the transfer window.
Inter Milan star Ivan Perisic has been backed to make the move so far, but a deal is yet to happen.
And Carragher does not think the Croatian would be a significant upgrade on the likes of Anthony Martial, Henrikh Mkhitaryan and Marcus Rashford.
“Ivan Perisic is a good player, but it doesn’t look like that’s going to happen and I think they’ve still got plenty of players who can play in those positions; Marcus Rashford, Anthony Martial, Henrikh Mkhitaryan or Juan Mata,” he said.