The 23-year-old has been training away from the first-team since he hit out at the Red Devils boss who had criticised his training levels.
Sancho took to social media in a now-deleted post to claim he has been made a scapegoat at the club after their 3-1 defeat to Arsenal.
talkSPORT understands United will continue to make him train away from the first-team if he still refuses to apologise to his boss.
He has now been barred from accessing all first-team facilities at their Carrington training ground.
Sancho's future with the club is certainly up in the air but O'Shea believes an apology would be the right thing to do.
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Speaking exclusively to talkSPORT, the former United defender said: "Yeah, obviously look it does [seems like an extreme punishment] but very simply for me, it boils down to an argument between the manager and a player.
"Ultimately, the manager generally wins and that's always been the case. If Jadon wants to get back playing football for United as quickly as possible, look maybe he might not mean it but just go and apologise.
"Then you're back involved in the squad and back involved with a chance to play. I know it's not ideal with how public it's been but it can be resolved very quickly."
Gabby Agbonlahor then asked what would happen if player was to take to social media and criticise Sir Alex Ferguson, to which O'Shea said: "You might have been banished from the UK, never mind the training ground!
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"On a serious note Gabby, if you go back to your time with Martin O'Neill, if you had an argument with Martin and you felt you were in the right, ultimately you'd still be going to apologise.
"In a sense it has to be that way because the manager has the lead from the front in terms of the discipline side of things to get hopefully everything right on the pitch as well.
"It's been a challenging start, a few injuries and a few decisions going against them haven't helped but they had a decent enough performance and win against Burnley and they'll be looking to carry that on against Palace."