The Argentina international has struggled to make a strong impact at the Santiago Bernabeu this season and there have been talks over a possible exit.
According to Spanish newspaper Marca, a Barclays Premier League side have made contact with Madrid over a possible move to sign the 23-year-old.
In fact, Di Maria have been offered a chance to triple his £1.65m-a-year salary at Madrid.
The club likely to fork out such extravagant packages is Manchester City, who are reportedly interested in adding the winger to their already illustrious ranks.
City lost out on Di Maria's signature to Madrid in 2010 and are now ready to prise him to the Etihad Stadium.
Not to be left out, Chelsea owner Roman Abramovich is also keen in joining the race to sign the former Benfica player as he is reportedly ready to sanction a £150million transfer kitty for Andre Villas-Boas.
Di Maria joined Madrid from Benfica in 2010 for €25 million.