The Portuguese coach is set to take charge at United after days of speculation linking him with the vacant role following Louis van Gaal’s sacking.
Mourinho has been out of work since being sacked by Chelsea back in December but has now secured an immediate return to the Premier League.
His first task at United will be to steer the Red Devils back to Champions League qualification after the Red Devils ended up fifth in the table last season.
But former Liverpool defender Carragher is expecting to see Mourinho have an instant impact at the club and get them challenging for the top-flight title.
Speaking on Sky Sports News HQ on Thursday evening, Carragher said: “They’ve got a chance of winning the league in his first season but they would have to bring in the right players in the summer.
“There’s no doubt that in 12 months he’ll be turning that squad into title challengers and after a year then maybe even title winners.
“The next season they could still win of course – you can’t put that past Jose Mourinho.”
Van Gaal was sacked on Monday, two days after United won the FA Cup.
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