The Argentina international is currently plying his trade at the World Cup with his home nation, but once the tournament finishes questions surrounding his future are due to be discussed.
Although he enjoyed a fine end of 2013/14, di Maria I rumoured to be surplus to requirements at the Bernabeu, with Los Blancos having been attracted towards a deal for Colombian star James Rodriguez.
Rumours in Spain have suggested that United are keen, and now it is also thought that the versatile attacking midfielder would be open to joining the Red Devils.
Offers of £40m are expected to be accepted, which Louis van Gaal can table despite having already splashed £60m on Luke Shaw and Ander Herrera.
Chelsea and Arsenal have also been linked with di Maria, but first-team opportunities are likely to be easier to come by at Old Trafford.