Rooney was not included in the hosts’ squad after injuring himself during United’s 3-0 victory at home to Hull City on Saturday, but Van Gaal said that he did not expect his captain to be out of action for long.
“It’s his knee, but we have to wait until tomorrow (Wednesday) to say anything about him because you never know with a knee,” Van Gaal told reporters at Old Trafford.
“My opinion is it’s not so serious, but I’m not a doctor. We have to wait for the scan, then we’ll know more. I hope it’s not so serious.”
Asked if the 29-year-old England star was likely to recover in time for United’s next game away to Southampton on Monday, Van Gaal replied: “I don’t think so, but you never know.”
The Dutchman was also upbeat about the hamstring injury that ruled record signing Angel di Maria out of the Stoke game, although the Argentina winger is also set to miss the trip to St Mary’s.
“Di Maria is not so serious, but he won’t play against Southampton,” said Van Gaal.
United’s victory over Stoke, secured by goals from Marouane Fellaini and Juan Mata, tightened their grip on fourth place and took them to within a point of third-place Southampton, who visit Arsenal on Wednesday.