Schalke have already axed 11 players and they are keen on releasing three more with the Ghana international among those mentioned.
Annan joined Schalke in the January transfer window from Norwegian side Rosenborg but has failed to impress since his move.
Veteran Gerald Asamoah, Ghana midfielder Anthony Annan and ex-Lille centre-half Nicolas Plestan are all set to leave the club soon.
“We are on a good path, but we are not finished yet. The next to depart could be Plestan, Annan and Asamoah,” Schalke sporting director Hosrt Heldt said to Bild.
Annan has also struggled recently in the Ghana national team as a toe injury has put Agyemang Badu ahead of him in the pecking order.
He could return to Norway but could also find suitors in France where Lyon had been interested in him in the past.
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