Reports emerging earlier this week suggest Besiktas are readying an approach for Ozil, with former board member Erol Kaynar claiming talks had been held with the German's agent.
However, in a post on their official Twitter account, the Gunners claimed there was no truth in the rumours.
"He is completely committed to the club. He is focussed on getting results," they said.
While talk of a move this summer might be premature, Ozil - who is of Turkish descent - revealed he might fancy a move to Turkey one day.
As a boyhood Fenerbahce fan, the Germany international rubbished talk of playing for Besiktas in the future but claims he would love to turn out for their rivals one day.
GETTY
Mesut Ozil has rubbished rumours of a move to join Turkish giants Besiktas
“In the future I want to wear a Fenerbahce shirt it would be an honour,” Ozil said
“Everyone knows I am a Fenerbahce fan.”
The 26-year-old remains pivotal to Arsene Wenger's plans this season and is under contract at the Emirates until 2018.
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Since signing from Real Madrid for £42.5million, Ozil has scored 12 times in 74 appearances.
Juventus were linked with the World Cup winner earlier in the transfer window but Wenger appears keen to keep hold of him.