Szczesny has spent the last two years on loan at Roma, where he has established himself as a first-team regular, but with David Ospina said to be leaving Arsenal in the summer, it remains unclear whether he will be required by the Premier League club.
However, the Polish international has insisted that no decision will be made regarding his future until the end of the current campaign.
The 27-year-old told BT Sport: "Staying at Roma? I'm happy here. I feel I've grown as a goalkeeper but for me, the time to make a decision will come in the summer.
"For now, I'm an Arsenal player, as soon as my loan finishes, I have to come back. I've always said I'd love to be back there.
"Like I said, what will happen definitely won't be decided now but in a month or two months' time."
Szczesny has featured in all of Roma's league matches during the current campaign.