It is understood that the Argentinian winger will complete a medical with United tomorrow morning and, if all goes to plan, the Barclays Premier League club will officially confirm his signing.
Di Maria was absent from the Real squad that beat Cordoba 2-0 at the Bernabeu last night.
United have made no official comment on the matter, but it is understood the agreed fee between the Red Devils and Real will eclipse the British record £50million Chelsea paid to Liverpool for Fernando Torres in 2011.
Should he sign, the 26-year-old cannot be involved in United's Capital One Cup tie at MK Dons tomorrow night, but could be set for a debut in Saturday's Barclays Premier League match at Burnley.
United appear in desperate need of a lift after a loss and a draw from their opening two league games and the man who was named man of the match in May's Champions League final would certainly give them that.
Di Maria, who will add pace and the ability to run with the ball, has been at the Bernabeu since 2010 after moving from Benfica.
United boss Louis van Gaal would neither confirm nor deny anything with regard to the Di Maria situation after his side's 1-1 draw at Sunderland on Sunday.
Van Gaal said: "I cannot say anything about transfers, you have to understand that. 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."
He added with a smile: "It is not only Di Maria - maybe (Arturo) Vidal or (Lionel) Messi! We are a big club."
The Sunderland game was United's second this season and, as in the 2-1 home defeat to Swansea the previous weekend, they put in an unconvincing display.
Taking a solitary point from six available has hardly made for the spectacular start to the Premier League campaign United fans might have hoped for after Van Gaal's arrival over the summer.
But striker Robin van Persie insists there is confidence in the camp that things will come good.
Van Persie told MUTV: "We've played two games and only picked up one point, we would have loved to have got six points but it didn't happen, so we have to bounce back.
"I think that everyone has faith and everyone believes in the staff and players.
"We have great players, and it's just a matter of time before the points will start coming in."
Van Persie was making his return to action at the Stadium of Light after an extended break following the World Cup, where he was part of Van Gaal's Holland side that came third in the tournament.
The frontman, who played for just over 60 minutes on Sunday, said of his condition: "I feel good, I feel fit.
"I had a good few weeks of training and played my first hour, so I'll look forward to the next game."
He added: "I worked with him (Van Gaal) for two years, and he's very clear.
"He's clear in what he asks of each player in the team every day. So, where I can, I will help the other players."