Given his sparse amount of game time all season, fans were shocked too see the Colombian named in the starting XI ahead of Petr Cech.
Only last month, Ospina had publicly declared his intent to leave Arsenal at the end of the season to find more regular playing time.
And now, speaking to talkSPORT before the final, Winter revealed the 28-year old planned to fly out to Turkey to hold talks with Fenerbahce the day after the final.
He said: "The fact is that Ospina's leaving for Fenerbahce.
"He's on a fast plane to Istanbul tomorrow, probably, so I find it very strange [that he started the FA Cup final]."