Evans aggravated an ankle injury whilst O'Shea sustained a heel injury in the 2-1 home win against Blackburn on Sunday.
"We won't know until Tuesday on the fitness of O'Shea and Evans," United boss Sir Alex Ferguson told the press on Monday.
"O'Shea is doing a light session on his own, but Jonny is unable to train.
"If neither of them make it then it will be time to panic. They are both big concerns for me but we have to accept that one or both might be missing and get on with it."