Real boss Carlo Ancelotti, who revealed earlier this week that Di Maria had told the club he wanted to leave and rejected the offer of a new contract, said the Argentina winger had not taken part in training on Sunday but had instead "come to say goodbye".
United have not made any official comment on reports that they are ready to sign Di Maria
It has been reported that the fee for the 26-year-old would eclipse the British record set by Fernando Torres' £50million move from Liverpool to Chelsea in 2011.
Ancelotti said: "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."
The Italian coach added: "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 manager Louis van Gaal has 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 believes Di Maria would "fit the bill" for the Red Devils
Neville told Sky Sports: "He can run and Manchester United haven't got any pace in wide areas
It is incredible
"That is what the club has been built on for the last 10 to 15 years - being able to get from box to box quickly, being able to spring on teams, having people that can dribble and are quick in the final third
"They have Adnan Januzaj but they really have lost that variety
"Last year the signings didn't fit the bill for me in terms of what United are and the philosophy
This fits the bill if they can get Di Maria
"The fans say a central midfielder or a centre-back is needed more, but I don't see any difference with a winger in that they need all three
"This is the first part of that - the correct signing, if they can get him."
Source : PA
Source: PA