The 25-year-old joined the Serie A club on loan from the Gunners at the start of the season and has started 27 league matches, with Arsenal having turned to Petr Cech ahead of the 2015-16 campaign.
Roma are yet to complete a deal to sign him permanently or renew his loan deal, meaning Szczesny – who says he is happy in the Italian capital – is presently scheduled to return to Arsenal.
"Everyone knows I'm really happy here," the goalkeeper told Sky Italia.
"I would like to be able to tell you about my future, but I don't know what it holds for me.
"I have expressed my intentions to the two clubs and now it's up to them. I have to decide what's best for my career."
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Roma are third in Serie A, five points clear of Inter with a game in hand at home to Bologna on Monday, meaning Champions League qualification looks likely.
"Since [head coach] Luciano Spalletti came in we have been superb," added Szczesny.
"Of course we want to secure Champions League qualification. We want to keep this run going that we have been on over the last 10 games.
"It's all about performing consistently. Hopefully we can finish on a high and make sure we qualify."