Jose is mostly about strong defense and then attacking if safe. As such, few players are given a defensive pass in his system - Ibra seems to be forgiven his lack of defense - anyone else?
Anyhow, Sanchez to United would likely not be a great fit - I can see Sanchez getting frustrated with Jose's very conservative tactics.
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At the same time, Pep does not tolerate laziness either - on offense, players need to move into space - on defense, players need to press intelligently to win the ball back quickly or if that fails move into good defensive shape.
Sanchez's personality and style of play seems to fit really well with Pep's philosophy and not nearly as well with Jose's.
Sanchez isn't a defensive slouch - but he doesn't strike me as someone content to bunker in on defense against the likes of us/Madrid/Bayern/PSG/Barca/etc.