The 28-year-old goalkeeper has previously stated that he has grown tired of his lack opportunities at Arsenal this season and will hold talks with Arsene Wenger over his future at the end of the season.
Ospina has made just one Premier League start this season and a further 11 in the FA Cup and Champions League so far.
Ospina does not want to spend another year on sitting on the bench with the risk of losing his place in Colombia’s 2018 World Cup squad.
The shot-stopper still has two-years left to run on his existing Emirates deal, but Arsenal are unlikely to stand in his way if he desires a move away from the club this summer.
Fenerbahce are understood to be leading the race but are only willing to pay around £2.5million for Ospina – less than half of what Arsenal paid for him three years ago.
Ospina’s potential exit means Arsene Wenger will have to decide whether to reinstate Wojciech Szczesny as back up to Petr Cech or promote Emiliano Martinez to second-choice goalkeeper at the club. The latter scenario seems more likely to happen as Szczesny left Arsenal to join Roma on loan for the past two seasons in order to play regularly – the Pole will not like the idea of playing second fiddle to Cech once again next season.