The Argentine international winger is expected to finalise his British record £59.7m move to United from Real Madrid today.
Di Maria flew in from Spain on Monday night and will now have a medical before completing a transfer which will make him the fourth most expensive player in football.
The fee agreed between the two clubs for the Argentina international eclipses the £50m Chelsea paid Liverpool for striker Fernando Torres three years ago.
In his post-match interview after Manchester United’s 1-1 draw at Sunderland on Super Sunday, manager Louis van Gaal declined to comment on speculation that Di Maria’s signing was imminent.
“The club has to announce it,” he told Sky Sports. “When we are thinking it is the right time for a transfer, then we come to you and say ‘OK, we have that player or the other player’. But at this time we cannot say anything.”
When asked if Di Maria is a player he would like to sign, Van Gaal confirmed he is but added: “I like Messi also and I like Vidal also so we have a lot of players in this world that I like but they cannot come always to Manchester United.”
Former Manchester United defender and Sky Sports football pundit Gary Neville told Sky Sports after United’s draw with Sunderland that he felt Di Maria was a good fit for Van Gaal’s side.
“It’s good business,” he said. “United have lost their negotiation strength but they just need to get the right players. This one is.
"He'll get pace into the game and get from box to box. He’s the right signing. You could argue they need other players in other areas but they definitely need a wide player.”
Madrid manager Carlo Ancelotti confirmed on Sunday the player had come to the club’s training base to bid farewell to his team-mates and the club’s staff.
"Di Maria has not trained with us and he came in to say goodbye to the players and people at the club," Ancelotti said.
"The decision is his and the club has done what it could to keep him here but he thought differently and so good luck to him. I am very happy with the work that he has done for Madrid but we have the chance to replace him well.
"We are thankful for what he has done at this club. There is nothing official yet but it is being sorted out.”
Football agent James Featherstone told Sky Sports News HQ on Monday that he expects more players to follow Di Maria to Old Trafford.
“I think they’ll certainly be looking to add to the squad,” he said. "It’s out there in the public domain that Louis van Gaal’s had some time with the squad now and he’ll look to add and complement the squad where he thinks appropriate.
“It’s a difficult time to add and obviously for Manchester United it’s been played out publicly for the last 12/24 months about their squad, so I’m sure they’ll be very patient they’ll only do it if the situation is correct to bring in players of the right quality for Manchester United.”