The Bernabeu star has been a long-term target for Sir Alex Ferguson, and is believed to be on his transfer shortlist for the end of the season.
But the report claims Inter Milan are keen to use the funds from the sale of Wesley Sneijder to bring Di Maria to the San Siro. Sneijder left the Serie 'A' club for Turkish side Galatasaray in the January transfer window.
The Argentina international joined the La Liga champions from Benfica in 2010, and has become a key part of Jose Mourinho's plans at the Bernabeu.
He was excellent against United in the Champions League last-16 first-leg on Wednesday, and often posed the biggest threat to the Premier League leaders with his direct running, close-control and slippery technique.
But the versatile winger has a difficult relationship with Mourinho, according to Spanish website fichajes.net, and another breakdown in communication with the Real Madrid boss could push him closer towards the exit door.
And the report suggests Di Maria would be likely to consider all offers on the table, should he decide to leave Real Madrid.
Manchester United are expected to sell Nani in the summer, while Ashley Young has struggled for fitness this season, which means the wide areas could be a possible area to strengthen for the Red Devils in the summer.
Antonio Valencia is out of form, and Sir Alex Ferguson has often opted to play Danny Welbeck, Wayne Rooney or Shinji Kagawa out-wide, with Robin Van Persie through the middle.