The 27-year-old has been in fine form for the Gunners these past few weeks following the injury to first-choice Petr Cech, starring in away trips to Tottenham Hotspur, Barcelona and indeed the Toffees as of late.
It has been Ospina's first real chance to prove what he can do this season, having played second fiddle to the former Chelsea man - Arsenal's only signing last summer - for so much of the campaign.
But the Colombian, who was linked with a move to the Goodison Park club in January (The Mail), is not thinking too far head, though, and states that he will not consider his future until the season is finished.
“Since Petr joined we have built a good friendship," he is quoted as saying by The Sun. “However, we are still competing for the spot.
“I don’t want to think about the summer. I’m focused on the present and my present is Arsenal. We will see how this season ends, then we will see what happens with my future.”
Ospina, contracted to Arsenal until 2019, has arguably done enough in recent weeks to suggest that he could well push Cech - six years his senior - very close for a starting spot next term.
Plus, Everton might come back in for this summer as they look to replace veteran goalkeeper Tim Howard, who will jet off to the MLS.