The Black Eagles have added Ospina to their goalkeeping shortlist – a position the Istanbul giants hope to strengthen over the winter break.
Ospina has struggled for playing time in the league for the Gunners but head coach Arsene Wenger has used the 26-year-old in the Champions League.
The Colombian keeper reportedly had a verbal agreement with Wenger that he would get game time in the Champions League despite the arrival of £10million keeper Petr Cech from reigning Premier League champions over the summer.
Ospina has been criticised for his performances in the Champions League and could end up being dropped for the Bayern Munich game this week.
The Metro report that the experienced keeper could leave Arsenal over the winter transfer window if dropped over the remaining Champions League games.
Besiktas were closely linked with Ospina over the summer but the deal fell through after Wenger decided to keep the keeper on at the North London based club.