The People says Diarra, who was released by the Londoners last summer, was set to win a new contract after recovering from a knee injury.
But manager Martin Jol has now decided against re-signing the former Real Madrid midfielder, amid fears over his long-term fitness.
Instead, the 32-year-old is poised to join Greek side Panathinaikos.
He said: "I can still play at a good level - but it won't be with Fulham."
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