The Argentinian international, 24, wants to double his salary to £80,000 a week after reportedly turning down Real's renewed offer of £70,000.
He is reportedly threatening to leave the La Liga giants once the season is over, unless he is paid a similar wage to his senior team mates.
The news has alerted Roman Abramovich who wants to bring a World Class wide player to Stamford bridge.
Di Maria signed for Real Madrid in 2010, joining from Benfica for a reported €25 million.
Source: DSG