Szczesny has helped Roma maintain a top-three position throughout the current Italian championship and two more points will see the Giallorossi secure a Champions League place.
And the 26-year-old feels his future lies in the Eternal City, telling Il Messaggero: "I want to stay.
"It's not all up to me, obviously. I want it to happen, and I know Roma and Arsenal are talking about it, so we'll see what happens.
"I'm happy to have helped the team and winning the title must be the next objective for this club."
Szczesny is twice an FA Cup winner with Arsenal but struggled for game time during the 2014-2015 Premier League season, with David Ospina often preferred.