The 28-year old, who arrived from the Emirates from Nice in 2014, has featured only 13 times this season.
Having fallen behind Petr Cech in the goalkeeping ranks, Ospina is keen to head to a club that can provide him with regular game time. Reports have shown that Turkish club Fenerbahce is keen on Ospina, and Arsenal has indicated they will not block any moves made for the Colombian.
Speaking to Turkish outlet Fanatik, Ospina said: "I told my club [Arsenal] that I want to go to a team where I'll play regularly.
"They know my intention. If the right offer comes, then I'll happily come to Turkey.
"My agent is taking care of transfer business. In fact, I'm happy at Arsenal but I have to play regularly. I told them exactly that.
"Arsenal's board told me they will not be making things difficult for me if the right offer comes in. Let's see what the future brings."