Hurriyet reports that Galatasaray have already reached an agreement with Real Madrid on the transfer fee.
The Spanish side have given Galatasaray permission to talk to Di Maria over a possible move.
Arsenal, Manchester United and Tottenham have also been strongly linked with a move for Di Maria.
Real Madrid could be forced to cash in on Di Maria in order to raise some of the expected £86million they are expected to pay for Tottenham winger Gareth Bale.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.