The Frenchman tweaked his knee during last weekend’s Community Shield in which they beat Manchester City 3-2.
"We'll give him until tomorrow but he is doubtful," manager Sir Alex Ferguson said.
One player who will definitely miss out is Mexican striker Javier Hernandez, who suffered a concussion during their pre-season tour of the United States.
"Chicharito is still, I would say, 10 days away from taking part in any football," said Ferguson.
"It's not a concern, just a precaution given the fact had a concussion a couple of years back."