Real Madrid are interested in signing De Gea this summer and contract talks between United and the Spaniard have so far been unproductive.
The 24-year-old waved to United fans as he left the pitch at Old Trafford last week after suffering an injury in the 1-1 draw against Arsenal.
But Van Gaal hopes that does not mean De Gea was saying farewell to the club he joined four years ago.
"I believe still that David de Gea shall stay," the United manager said.
De Gea is in contention to start the final match of the season at Hull on Sunday despite the hamstring injury he suffered against the Gunners.
Following the 1-1 draw against Arsenal, Van Gaal sounded pessimistic about the chances of the Spain goalkeeper staying at the club.
Two days after saying United had drawn up a list of potential replacements for the player, the United boss admitted the lure of returning to his homeland may end up being too strong.
Van Gaal said in his post-match press conference: "He is Spanish and his girlfriend is Spanish, now a Spanish club is coming, his father and mother come every week or every two weeks here, so it is difficult
But we would be very happy if he stays."
But it sounded like Van Gaal was far from resigned to losing the player when speaking at his pre-match press conference at Carrington on Friday ahead of the season finale at the KC Stadium.
"First we have to wait and see if De Gea is leaving
After that we shall talk about the other things," he said.
De Gea was expected to miss the match at Hull, but it has emerged that he is in contention to start.
"I want to play him against Hull City because of the fact that I have to put out my strongest team," Van Gaal said.
"And I think with David de Gea we have the strongest team."
Van Gaal will see how De Gea performs in his final training session before making a call on whether he starts.
Van Gaal said: "He has trained today for the first time
He still had a problem so we have to wait and see tomorrow
I cannot say that he is able to play, I have to wait and see."
Source : PA
Source: PA