De Gea is entering the final year of his contract at Old Trafford and has been continually linked with a move to Madrid this season.
The issue has been exacerbated by the player’s refusal to confirm the reports one way or the other.
Van Gaal is optimistic that De Gea may yet decide to reject Madrid before signing a new deal at United.
Van Gaal: "I believe still that David de Gea shall stay."
— MUFC Peoples Person (@PeoplesPerson_) May 22, 2015
De Gea faces a late fitness test for the game against Hull City this weekend, which may end up being his final appearance in a United shirt.
The Spaniard is adored by United fans and it would be come as a bitter blow if he was to leave the club.
Meanwhile, Madrid supporters continue to boo the likes of Iker Casillas and Gareth Bale following a few average performances. Hopefully De Gea realises he will not get the adulation at Madrid that he currently gets at United.