Diame was stretchered off in the second half of West Ham's 3-2 defeat to Liverpool after pulling up with the problem.
It was initially feared that the all-action midfielder could be sidelined for up to three months with the setback.
However, Diame, who has a release clause of £3.5million in his contract, has told Sky Sports News that the injury is not as serious as first feared and hopes to be back in action in January.
The news will come as a massive boost to West Ham with Diame establishing himself as the club's stand-out performer so far this season.
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