Mourinho has been heavily linked with a move to Old Trafford since he was relieved of his duties at Chelsea last week.
Following a string of poor results, van Gaal is under huge pressure at Man United and there have been numerous calls for him to be sacked. However, Carragher believes Mourinho would not fit United due to concerns over his playing style and record of bringing through young players.
“Is Jose the perfect fit for United? I say no,” Carragher said.
“The reason is that if I have to imagine Manchester United over the last 50-60 years and what they are about; winning trophies, Jose massively ticks that box; but bringing young players through? No. Playing exciting, cut throat football, going for every game? He doesn’t tick that box either.
“If that is someone that they go for, I think it’ll show the fear Manchester United’s board have of other teams getting away from them. There’ll be that thought of Pep Guardiola maybe going to Manchester City and they’ll be thinking we’re actually falling behind.
“They’ll forget some of the principles that have made the club over the last 50 or 60 years; and they’re just that desperate to get to back winning trophies.”
Mourinho is rightly regarded as one of the best managers in the world but there is a question mark over his long-term suitability and whether or not he actually leaves a club in a better state than when he started.
It is a crucial period for United and you get the sense that the decision that they do (or do not) make will have a major impact on the club in the coming years.