Anelka joined Shanghai from Chelsea in the last January transfer window, but has struggled to make an impression in Chinese football.
He was joined in the Far East by former team-mate Didier Drogba after the Ivorian decided to leave Stamford Bridge after helping the Blues to win the Champions League.
However, Shanghai could only finish ninth in the Super League and, after scoring just three goals, Anelka is now in talks to leave the club.
"The discussion is between the club and himself, I don't know about the specific details," said Shanghai spokesman Ma Yue.
"But so far we haven't got the final result."
Reports are suggesting that Anelka is prepared to give up the final year of his contract on the proviso that Shanghai will grant him a free transfer.
The 33-year-old has been strongly linked with a return to the Premier League, with Queens Park Rangers and West Ham United both reported to be considering an offer.
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