The 24-year-old De Gea, who is seen as the perfect replacement for the ageing Iker Cassillas at the Bernabeu, has enjoyed a fine season and won the club's player of the year award on Wednesday.
Speaking ahead of United's final game of the season against Hull City on Sunday, Van Gaal said De Gea, who suffered a hamstring injury in the draw against Arsenal last weekend, has not packed his bags just yet.
“I believe still that David De Gea will stay,” Van Gaal told a news conference on Friday. “I want to play him in the match against Hull City because I have to put my strongest team.
“David has trained today for the first time. He still has a problem so we have to wait and see.
“I have spoken to some players this week. You have to wait and see how these talks develop in terms of players staying or going.”
Hull must beat Van Gaal's side on Sunday and also hope 17th-placed Newcastle United fail to defeat West Ham United to avoid relegation to the Championship.
Hull boss Steve Bruce spent nine years as a player at Old Trafford but Van Gaal, who will be able to recall captain Wayne Rooney after injury, said it was important United do not go easy on their former employee.
“It's the same approach as ever. We need to defend our image as Manchester United and we are ending in fourth position, so we have to give our utmost best,” the Dutchman said.
“I have to put my strongest team because we have to give everything for all the other Premier League clubs, and especially of course Newcastle United.
“We have taken six points off Newcastle United and we have to take six points off Hull City, I think. I have said to the players in spite of him (Bruce) being a Manchester United guy, we have to do what everybody is expecting from us.” – Reuters
Original source: Van Gaal confident De Gea will stay