De Gea went off with a hamstring injury during Sunday's 1-1 draw with Arsenal at Old Trafford, which makes him a doubt for United's last match of the season at Hull City next weekend - and means he may have played his final game for the club.

Real have earmarked the 24-year-old Spain international as the successor to veteran keeper Iker Casillas, and he is sure to be tempted by the possibility rejoining his family and girlfriend in his homeland, according to Van Gaal.

The Dutchman said he did not know if Real had made an offer but added: "De Gea is Spanish, he is a Spanish international.

"He is still behind Casillas but now a Spanish club is coming. His girlfriend is Spanish and his father and mother come over every week or two weeks to watch him - it is difficult for him."

Real dropped Casillas for their win at Espanyol on Sunday, but stand-in Keylor Navas was badly at fault as Barcelona won La Liga.

The United boss insisted he would not be doing any more to persuade De Gea, who has one more season left on his contract, to sign a new deal, explaining: "I don't think I can persuade him because he knows everything that he has at Manchester United at this moment.

"I don't have to say anything for the benefit of Manchester United because he can feel everything. The crowd has been unbelievable. You have seen that reaction here. It has been unbelievable, for the team and for him individually.

"When he is going he is losing that because here he has a lot of credits."

Van Gaal added: "A transfer is a process involving a player, a club and his present club. He has to choose.

"It is not easy to choose between two great clubs. We would be very happy if he stays. Of course he is Spanish and his girlfriend is Spanish and he can go to another great club, so it is difficult for him to decide.

"David De Gea shall not leave us so easily because we are a great club and he wants to participate."

Falcao future in doubt

Van Gaal must also make a decision about on-loan Monaco striker Radamel Falcao, who appeared to wave goodbye to the Old Trafford crowd when he was substituted 60 minutes into another disappointing performance.

The manager said: "You know the situation with Falcao. At the end of the season, we shall decide. You have to ask him if he was waving goodbye and then quote him. You are only assuming."

Champions League qualifier 'stressful'

Sunday's draw means that Manchester United are likely to finish fourth in the table, meaning they will face a two-legged Champions League qualifier in August.

Only the Premier League's top three sides qualify automatically for the group stages.

Van Gaal said: "We have not yet qualified for the Champions League. It is always stressful as you can meet an opponent who is halfway through a season already. It is not so easy.

"I am satisfied we have set our goal and reached that. From what I have seen of the fans, they are pleased. But I want more as manager. Next year we will fight for more."

'We must learn to finish games'

(BBC)