Ozil had arguably his worst season at Arsenal in the 2018/2019 campaign, making just 24 Premier League appearances, as he found himself in and out of the team on several occasions.
The world cup winner’s relationship with manager Unai Emery has not been the best with Ozil being left out of some of Arsenal’s biggest games of the season.
It had been suggested that Ozil’s days at the Emirates stadium might be numbered with Arsenal looking to offload him to reduce their wage bill.
Fenerbahce were strongly linked with the former Werder Bremen playmaker, who currently earns £350,000 a week at Arsenal, but their unhealthy financial status has put them off in brokering a deal for the German.
A statement from the Super Lig side read: "Mesut Ozil, with his career and standing, successfully represents our country abroad (Ozil is of Turkish ancestry). 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."
Fenerbahce endured a tough campaign in the Turkish top flight last season as they flirted with relegation for majority of 2018/2019 until an upturn in form saw them stumble to a sixth place finish.