Ozil joined Arsenal from Real Madrid in 2013, and although he has been a key player for much of that time, he has also polarised opinion among the club's supporters.
After an underwhelming season under Unai Emery last term, media speculation had suggested Arsenal are willing to offload Ozil in order to lighten their wage bill, but Fenerbahce insist rumours of a loan move are wide of the mark.
A Fenerbahce statement read: "Mesut Ozil, with his career and standing, successfully represents our country abroad. He is an important value known with the identity of Fenerbahce.
"However, Fenerbahce does not have a proposal for Mesut Ozil. Under the current economic conditions, such a step is not possible for both parties.
"Our president, Ali Koc, made statements on the subject in the WinWin program held on June 20 and emphasised that this could not be realised in the short term."