The Red Devils are believed to be long-term admirers of the 25-year-old, and are even rumoured to have attempted to bring him to the Premier League during his time at Benfica.
Although he is widely regarded as one of the top wide forwards in European football, Real are said to be willing to allow him to leave this summer after a forgettable season so far.
Di Maria’s agents are reportedly trawling the continents biggest sides in an attempt to find a party willing to make a move later this year.
Big spending French outfit Paris Saint-Germain are believed to be interested, and would certainly have the financial muscle to lure the South American to Ligue 1.
However, the prospect of Premier League football could put United at the top of the list.
With Nani’s future at Old Trafford far from certain, Sir Alex Ferguson may attempt to bring in Di Maria as a direct replacement.
Having paid in excess of £20m for his signature in 2010, Real are likely to be looking to recoup the majority of their investment, a demand that United would be able to match.