The free agent has also been linked with Celtic this season.
The west London club are expected to deal in free transfer and loan deals during the winter window but the Mail state that Diarra has options to return back to Russia.
The Frenchman has been linked with Celtic this season and reportedly almost joined QPR in the summer.
In an interesting twist, however, Diarra has been training with West Ham United's head of medicine Stijn Vandenbroucke, whom he previously worked with at Anzhi Makhachkala.
It may simply be something perfectly innocent in the fact that the 29-year-old is working with the West Ham man to up his fitness, although the Mail claim that, 'if anything, Diarra would prefer to move to Upton Park.'
It appears for now, though, that Diarra won't be joining QPR, West Ham or Celtic. The Frenchman is clearly a midfielder of value - and had plenty of ability in his prime. But the fact that he came close to joining the R's, as well as SPL champions Celtic, does not seem to count for anything with regards to his future.
All we can concretely say at the moment is that Diarra is working with a member of West Ham's staff - but only for training purposes.