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 does not think that was a sign from De Gea that his four-year spell at United was up.
”I believe still that David de Gea shall stay,” the United manager said.
Following the stalemate against Arsenal, Van Gaal sounded somewhat more pessimistic about his star keeper, who was named club player of the season this week for the second year in a row.
Two days after saying he had drawn up a list of potential replacements for United’s player of the season, the Dutchman admitted the lure of returning to his homeland may end up being too strong for De Gea. Van Gaal said in his post-match press conference last weekend: ”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 there was a more optimistic tone from Van Gaal when he spoke at Carrington ahead of the clash with Hull.
The Spain international may even take the gloves back off Victor Valdes, who replaced De Gea after he suffered his hamstring injury.
”I want to play him against Hull City because of the fact I have to put out my strongest team,” Van Gaal said.
”And I think with David de Gea, we have the strongest team. I think De Gea is a better goalkeeper (than Valdes).
”He (De Gea) has trained today for the first time. He still had a problem so we have to wait and see tomorrow.” It is not just De Gea’s future that has been the source of speculation over the last few weeks.
A number of players still have question marks over their futures. Robin van Persie, Anders Lindegaard, Rafael, Jonny Evans, Nani, Adnan Januzaj, James Wilson, Radamel Falcao, Nani and Javier Hernandez all could be playing their football elsewhere next year — either on loan or permanently.
Van Gaal has spoken to a number of them about their futures already and will conclude discussions over the weekend.
”I shall talk with them, maybe tomorrow,” Van Gaal said.
”We have a farewell drink after the match. I have the Monday to talk, and I have already this week for some players to talk, so I shall do that.
”You have to wait and see how these talks develop in straying or going away.”
After those discussions end, Van Gaal will fly to his villa in the Algarve for a well-earned rest.
The 63-year-old had just two days off after the World Cup so he is looking forward to a break, but his phone will be close by his side just in case he is needed for any transfer business.
“Immediately after the match, we will have a farewell drink and after that, we have a recovery day, and then we go off,” he told MUTV.
“All the players have to fly out to international duties but I will go on holidays and I’m willing to go to my paradise in Portugal.”
Asked if all transfer business will be left to executive vice-chairman Ed Woodward during that time, Van Gaal said: “No, not to Ed because you also have a telephone and computer, so we are always in contact.
“As a manager, you never have holidays but I am in a better climate than here in Manchester. I am sorry to say that!”
Van Gaal, who has Wayne Rooney available for Sunday’s match, wants to end the season on a high, even though he knows victory against Hull would mean relegation for former United defender Steve Bruce. Van Gaal added: ”I have said to the players in spite of him being a Manchester United guy, we have to do what everybody is expecting from us.
”We have the same approach as ever. We have to give our utmost best.“