The Real Madrid midfielder arrived in the northwest of England late on Monday night and was shown around United's training ground and facilities.
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Medical officers have been on site since early on Tuesday morning and Di Maria will now be put through his paces before finalizing the biggest deal in British football history.
The Argentine will be the club's new No.7 and a replica jersey with his name and new number has been prepared for photo opportunities following the conclusion of the medical.
The 26-year-old will then be officially confirmed as a United player after putting pen to paper on a massive contract which could earn him more than €376,000 per week, including a €6.3 million signing on fee and bonuses.
Ander Herrera, Luke Shaw and Marcos Rojo have already sealed moves to Old Trafford, and more are expected to follow Di Maria.
United has been closely monitoring Juventus midfielder Arturo Vidal all summer, and has been linked with a formal bid in Tuesday's newspapers after manager Louis van Gaal mentioned him by name following Sunday's draw at Sunderland.
Di Maria has been a key part of Madrid's recent success and was named man of the match in May's Champions League final triumph against Atletico Madrid.
He scored one goal at this summer's World Cup as Argentina reached the final, only to be beaten by Germany in Rio de Janeiro.
Since joining from Benfica in 2010, the first season of Jose Mourinho's reign at the Santiago Bernabeu, Di Maria has scored 22 goals in 124 league appearances, and is the third highest assist maker in Europe's major leagues, behind Lionel Messi and Mesut Ozil.
He is now set to move ahead of Fernando Torres, who moved to Chelsea for €62 million in 2011, to become the most expensive footballer in Britain.