It would be interesting to see statistics on those players who have gone out on loan and come back to the club and been successful and stayed.
He is learning his trade and among some top players plus one would believe a top coaching staff.
So he goes out on loan to a lesser premier club or a championship club he may play more games but would that improve his skills to play at a higher standard, i.e., European level.
There is a possibility that he has reached his full potential, ability and level that with further coaching and game time he will not improve to make that leap from squad player to be a continuous first team choice at Utd. However, watching him this season he has made progress, further coaching on his weak areas will improve him further, training with top players will enhance the coaching, maturity will also improve his all round game.
So no I think he should stay, listen, take note of his coaching staff and work hard, improve his all round game and remember that he is 20 years of age learning his trade at one of the top clubs in the world.