Reports from Argentina carried by the Daily Express claim a Di Maria source has confirmed that Arsenal, Monaco and Paris Saint Germain are the three teams to make firm offers for the Real Madrid winger.
Manchester United and Manchester City have been long-term admirers of the Argentina international, and the report goes on to claim that he's resolved to leaving the Bernabeu following their Champions League triumph this month.
Real Madrid are thought to be desperate to keep Di Maria if possible, but competition for places is intense and the Argentine may feel he stands a better chance of more regular starts elsewhere.
A source told Argentinian based UOL Sport: "It is true that he is leaving because he wants to go. It is very likely that he will leave before the end of the World Cup in Brazil.
"Arsenal, PSG and Monaco have all made concrete offers for Angel. But there is still interest from Manchester City, Manchester United and Juventus."
The 26-year-old attacker has played an important role under Carlo Ancelotti and the report goes on to claim that Cristiano Ronaldo is also keen for Di Maria to stay put.
Arsenal and Manchester United may end up battling each other to bring him to the Premier League, but they may have to pay a heavy price.
A recent report claimed that the Spanish giants could demand £32.5m for his signature this summer with interest so high.