The Portuguese coach is set to take over at Old Trafford after being identified as the man to guide the Red Devils back to the top of English football.
Mourinho has a history of not placing much faith in younger players as he prepares to take over at Old Trafford.
The likes of Marcus Rashford and Timothy Fosu-Mensah both earned plenty of new admirers for their impressive form under Louis van Gaal last season.
But former Liverpool defender Carragher feels that Rashford, 18, will have nothing to worry about under his new manager as long as he continues to produce similar performances to last season.
Speaking on Sky Sports News HQ on Thursday evening, Carragher said: “As a young player, you’re always concerned and Van Gaal thought highly of him [Rashford].
“But now he’s got to prove himself again. But if he continues in the same vein of form, he will be fine. The way he’s playing, you can’t leave him out no matter who the manager is.
“The most important thing is for United is to start competing for trophies and there’s no one better on the market for doing that than Jose Mourinho.”
United opted to sack Van Gaal on Monday after they finished fifth in the Premier League and won the FA Cup.
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