Several British media reports earlier on today said that 30-year-old striker Rooney, also the captain of England, would be sidelined for up to two months.
Previously, United confirmed Rooney would miss their Europa League game at FC Midtjylland on Thursday.
He was not in van Gaal's 18-man squad which travelled to Denmark today for the first leg of their last-32 tie and a United statement said Van Gaal would provide further details at his pre-match press conference.
"It's difficult to say but he's injured in the game versus Sunderland and has a knee problem. We have to wait and see how long that takes. I cannot say," the Dutch manager added.
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"He scores a lot of goals so he is very important for us. We know that but we have to cope with that.
"Certainly in 2016, he has scored and that's why we had a good run in matches until Sunderland. But we have to cope with that. Everybody can be injured and also the captain can be injured."
United's 2-1 loss to Sunderland last weekend left them fifth in England's top flight and six points off the top-four spot -- the club's "minimum requirement" in the under-pressure Van Gaal's words -- that would secure entry into next season's Champions League.
They have 12 rounds of Premier League fixtures left in which to overhaul fourth-placed local rivals Manchester City, who have already announced that Bayern Munich boss Pep Guardiola will be their new manager next season.