The France midfielder has been strongly linked with football away from the Santiago Bernabeu after being relegated to the club's periphery under coach Jose Mourinho.
Fenerbahce have been suggested as Diarra's likeliest destination, but fresh speculation suggests that the midfielder has reached an agreement with Galatasaray after a meeting between the club and his brother.
It is reported that the 27-year-old is ready to sign a €5.5 million-a-year contact, a considerable improvement from his current annual salary of €4m.
Galatasaray must now open talks with Real Madrid regarding the midfielder's transfer, with the Turkish club ready to offer up to €8m for the player.
The former Portsmouth midfielder, who joined Madrid in 2009, has made 25 competitive appearances to date in 2011-12.
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