Reports suggested that an agreement had been reached between United and Real for the Red Devils to splash out 75 million euros (around B£60million) plus add-ons for Di Maria, and that the Argentina international would fly to Manchester on Monday.
And 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".
However, Van Gaal gave little away on the matter when asked about it after his side's 1-1 Premier League draw at Sunderland.
"I cannot say anything about transfers, you have to understand that," he 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.
"He has come and has not practised. It's not official yet, but he came to say goodbye," he said.
"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 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.
Former United captain Gary Neville feels Di Maria fits the bill for the Red Devils, but that they are "over-paying", with their negotiating position having been hampered by their 2-1 home defeat to Swansea in Van Gaal's first competitive game in charge last week.
Neville said: "It's good business if they get the right player.
"They're overpaying for him, but they've lost their negotiating strength.
"They just need to get the right players. Last year they overpaid for two players that I don't believe fit the philosophy of the club. This one does: he can run, he can get from box to box quickly, he'll inject pace into a game, and I think it's the right signing.
"You can argue they need players in other areas of the pitch as well but they definitely need a wide player. I think he'll play as one of the front three.
"With that defeat to Swansea they lost their negotiating strength.
"The call that every club in Europe wanted was from Manchester United, because they need two or three players.
"They need a central midfield player, they need a centre-back and they need a winger, so Real Madrid know they can bung the price up."
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