The Yellow Canaries are reported to be in talks with the Colombian international’s agent and the Gunners are expected to give Ospina the green light to make the move following the arrival of Petr Cech.
Ospina will fall down the pecking order behind Cech and Wojciech Szczesny to become the Gunners third choice keeper were he to stay at the club next season.
The 26-year-old keeper is currently on international duty with Colombia who booked a place in the Copa America quarter-finals following a goalless draw against Venezuela at the start of the week.
Speaking to reporters after the game Ospina refused to directly talk about a move to Fenerbahçe and instead told journalists to speak with his agent.
“They are dealing with my agent. But at the moment, the only thoughts I have are for Colombia — I will not betray my team,” he told the Evening Standard.
Ospina joined the Gunners on £3 million move from Ligue 1 outfit Nice last season and kept 10 clean sheets in 23 games for the North London based outfit.