The Yellow Canaries are expected to face competition from Bayern Munich who are also closely linked with the World Cup winner in the report.
Ozil has made no secret of his desire to play for his childhood club Fenerbahce at some stage in his career but he still has another two-and-a-half years left on his current contract and it will take a record bid from the Istanbul giants to prize him away from Arsenal.
Speaking to the Sabah newspaper Ozil recently confirmed that he has always been a Yellow Canaries fan to the Turkish newspaper.
“Everyone knows I am a Fenerbahçe fan,” he said.
The report also claims that Arsenal are close to agreeing a record £51.1 million contract extension deal with the 27-year-old which would cement his long term future in north London.
Should Arsenal go ahead with finalising the five-and-a-half year deal it would make him the highest paid player in club history.
Ozil is reported to be happy at Arsenal and has been in great form providing 12 assists in his last 14 league games. The World Cup winner also broke the record for providing assists in consecutive league matches this season (7).