The ex-Germany international has previously stated that he would see out the remainder of his Emirates contract, but an exit in the January window now appears to be the most likely outcome.
Speaking to Canal+, Koc said: "Let me tell you the latest on Mesut Ozil. We've said it would be a dream for Fenerbahce. The club knows what the coach wants and our transfer policy is guided by that. There hasn't been an official announcement.
"What I can say is we are closer than before. There may be a resolution, there may not be a resolution. Fenerbahce SK will make the announcement when the time comes."
Ozil was eligible to play against Newcastle United in the FA Cup, but he was not selected by Mikel Arteta and looks set to leave Arsenal having amassed 44 goals and 77 assists in 254 appearances.