The attacker's Argentine representative Eugenio Lopez has suggested there is bad blood with president Florentino Perez as the player continues to be linked with a move
The 25-year-old has been the subject of intense speculation in recent weeks with reports suggesting he is unhappy at the club, although Carlo Ancelotti made it clear he has no plans to allow the winger to leave Santiago Bernabeu.
However, Eugenio Lopez - the player's representative from his native Argentina - has now hinted at tension between Di Maria and president Florentio Perez, claiming there are several top sides waiting in the wings should he decide to quit the Spanish capital.
"Angel has a contract until 2018. Many clubs want him. There is a presidential matter, but I don't want to talk about it," he told radio program La Red.
Di Maria, who joined the club from Benfica in 2010, has four goals and seven assists in 19 appearances this season.
Monaco coach Claudio Ranieri has previously voiced his admiration for the player, who signed a new contract with Madrid just last year.