"Mesut Ozil, with his career and stance successfully representing our country abroad, is an important value known within the identity of Fenerbahce," the statement read, with translation from The Telegraph's Sam Dean.
"However, Fenerbahce does not have an initiative for Mesut Ozil. Under the current economic conditions, such a step is not possible for both parties."
The midfielder has won 92 caps for Germany but has Turkish origins. The president of the transcontinental country, Recep Tayyip Erdogan, was the best man at his wedding in June.
Despite his strong affiliation with Turkey and transfer links with Fenerbahce - who hail from the Asian side of Istanbul - it seems his wage demands are a major hurdle for clubs negotiating Ozil's transfer from Arsenal. The World Cup winner is understood to receive £350,000 a week in north London.
Additionally, the fact he turns 31 in October and his Gunners contract doesn't expire until 2021 significantly reduces the number of clubs prepared to splurge on the FC Schalke product.
Ozil joined Arsenal from Real Madrid for £42 million in 2013 and has since hoisted the FA Cup on three occasions while appearing 166 times in the Premier League.