The Morocco international is leaving Gala in January after falling out with coach Okan Buruk and club management.
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The former Ajax midfielder has been linked with a return to the Eredivisie.
However, H24 says Ipswich and West Ham are also watching developments around the ex-Chelsea attacker.
Ziyech said earlier this week: "Galatasaray, it's over for me, I told them I'm leaving in January. They don't ask me anything anymore, I do what I want.
"I've never seen such a bad coach as Okan Buruk. If Galatasaray can win the title? I don't care... Leave me alone, no matter what happens. I already regret coming.
"I was supposed to leave at the beginning of the season, but they didn't want to. I'm leaving in January."