Mourinho has pledged to name a strong line-up against the Latics but will call upon his impressive depth, with Martial and Shaw among those set to come in.
Martial's happiness has been questioned recently and the United boss confirmed the Frenchman will get a chance to shine on Sunday, having been omitted from the last two match day squads.
Asked how the France international took being left out at Hull, Mourinho said: "I don't know. I don't speak with the players about how they take it.
"He will play Sunday and if Sunday he plays magnificently, he will play against Hull City in the next match. It's simple."
Shaw is also set to get a chance to prove his worth on Sunday after belatedly returning to the United squad at Hull.