De Gea has enjoyed a fine season for the Red Devils so far, and has attracted serious interest from the Champions League winners.
The Spaniard's influential agent, Jorge Mendes, recently hinted that a summer move could be on the cards by saying "things change every five minutes".
And when asked if Madrid could make their move, Van Gaal said: "In football, everything is possible. We want to keep him."
The Dutchman also responded to questions about his team's recent performances after they managed just three goals in their last four Premier League matches, and he admits fans are not being entertained.
“The last matches, we failed to do that because it’s the goals that are the most important thing and the fans are enjoying the goals the most," he added. "So, when we are not scoring too much, you cannot enjoy the game.
"We have a lot of players who are attractive to see, so I don’t think we are not attractive enough, but we have to score more goals, especially when you see the last games.
"We have to improve in our attacking organisation and finishing the chances is always the most important thing because it is only goals that count."
