Spanish newspaper Marca on Sunday evening reported an agreement had been reached between United and Real for the Red Devils to splash out 75 million euros (around £60million) plus add-ons for Di Maria, and that the Argentina international would fly to Manchester on Monday.
Earlier on Sunday, Real boss Carlo Ancelotti - a few days after revealing Di Maria had told the Spanish outfit he wanted to leave and rejected the offer of a new contract - said the 26-year-old had not taken part in training that morning but instead ''come to say goodbye''.
Meanwhile, Van Gaal gave little away on the matter when asked about it after his side's 1-1 Barclays Premier League draw at Sunderland.
"I cannot say anything about transfers, you have to understand that," the Dutchman said.
"When a transfer has been finished then we can say something.
"But now you have to wait and see
When the moment is there Manchester United shall announce it."
When asked if he was interested in bringing Di Maria to Old Trafford, Van Gaal said that could be said for several players.
"It is not only Di Maria, maybe (Arturo) Vidal or (Lionel) Messi! We are a big club," the Dutchman added.
Ancelotti's comments suggested the deal is drawing close.
The Italian said of Di Maria: ''He has come and has not practised
It's not official yet, but he came to say goodbye.
''We gave thanks for what he has done for this club and wish him luck for the future
It is not official, but it is solved.
''I have personally had a good relationship with him and he did a fantastic job here.
''It was his decision to leave because the club did everything possible for him to stay by offering everything to him to stay.''
Manchester United have already signed Di Maria's international team-mate Marcos Rojo this summer, while the club have also brought in another defender in England's Luke Shaw and Spanish midfielder Ander Herrera.
The British transfer record currently stands at £50million, set by Fernando Torres' move from Liverpool to Chelsea in 2011.
Source : PA
Source: PA