Former Germany international Ozil, who has Turkish origins, has been linked with the Super Lig club this summer.
The 30-year-old is the Gunners’ highest-paid player, having signed a £350,000-a-week contract in 2018.
“Under the current economic conditions, such a step is not possible for both parties,” said a Fenerbahce statement.
Ozil was signed by Arsenal from Real Madrid for £42m – a club record at the time – in 2013 during former Gunners manager Arsene Wenger’s tenure.
However, under Wenger’s successor Unai Emery, he was sparingly used last season, making 35 appearances and scoring six goals.