The Old Trafford club has made a breakthrough in its pursuit of the Real Madrid winger, with negotiations set to continue Sunday.
Madrid coach Carlo Ancelotti has confirmed the player will leave the club this summer and it is understood United has edged closer to the signing of the Argentina international, who is keen to link up with Louis van Gaal.
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Madrid is aiming to receive somewhere in the region of 80 million to 90 million euros for Di Maria, though the initial fee paid by United could be lower with bonuses and add-ons supplementing the deal.
Di Maria, meanwhile, could pocket a 6 million euro signing-on fee and sign a five-year contract worth close to the 375,000 euros a week earned by Wayne Rooney.
United has secured just three signings this summer, bringing in Ander Herrera from Athletic Bilbao for around 35 million euros, left back Luke Shaw in a deal that could rise to 38 million euros, and 20 million euros for Argentina defender Marcos Rojo.
After a disappointing transfer window so far, the pressure is on Old Trafford executive vice chairman Ed Woodward to complete a move for Di Maria.
Indeed, Woodward is understood to be desperate to seal the signing of the winger, who has been a target for United over several weeks.
Di Maria has moved ever closer to a Madrid exit as the start of the new season in Spain has approached.
The winger was not in the squad for the second leg of the Spanish Super Cup defeat to rivals Atletico, and Madrid boss Carlo Ancelotti has confirmed the player has said his goodbyes ahead of his departure.
"Di Maria has not come here to train, just to say goodbye," he told reporters. "It's not official yet, but everything is being sorted. We thanked him for what he has given the club and we wished him good luck. I have had a very good relationship with Di Maria. He has done a fantastic job at Real Madrid. We are able to replace him very well.
"It was his decision, because the club did everything possible to keep him, offering everything we could to have him here. He decided otherwise, so good luck to him."
Negotiations to complete the deal are set to continue Sunday.