Per Goal's Ryan Benson, they heaped praise on the midfielder but also threw cold water on the speculation:
"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."
According to Benson, there were reports Arsenal could move Ozil to Fenerbahce in a loan deal in an effort to get his wages off their books.
Fanatik (h/t Metro) reported such a move would not include a loan fee, and Arsenal would still pay £5.5 million of his £13.5 million wages.
Since signing that contract, Ozil has fallen out of favour at the Emirates Stadium. His inconsistent play has not warranted his gaudy wages.
According to Spotrac, his salary of £350,000 per week is nearly double that of the second-highest earner at the club, with Pierre-Emerick Aubameyang coming in at £200,000 per week.
The 30-year-old has not indicated he wants a transfer this summer, and he has kicked off his pre-season with the Gunners:
A transfer to Turkey could be appealing, however. While he was born and raised in Germany, Ozil is of Turkish descent and has a personal relationship with the nation's president, Recep Tayyip Erdogan.
When the midfielder got married this summer, Erdogan acted as his best man:
The likes of Robinho and Ricardo Quaresma have found a home in the lucrative Super Ligin recent years, and Fenerbahce could use all the help they can get after struggling to a sixth-placed finish last season.
It would appear Ozil doesn't fit their budget, however, unless he's willing to sacrifice some of his big wages to facilitate a move.