The 26-year-old spent the best part of five seasons between the posts at Arsenal but Petr Cech's arrival in 2015 meant he was loaned out to the Giallorossi.
Having spent one season with Roma, the Poland international then extended his stay for another year and he has helped the capital club to second place in the Italian top-flight standings.
The Eternal City side are four points behind table-topping Juventus but Szczesny feels they can challenge the Old Lady for honours.
However, they must first get through a tough Derby della Capitale on Sunday afternoon.
"I returned to Roma because I want to win. There are still many games, anything is possible," he told Corriere dello Sport. "But for now, it’s better to think about the derby. If we win, we’ll be one step closer to our ultimate objective.
"You have to take one step at a time, you have to try to take three points from every game.
"I don’t want to think too far ahead as we’re still six months from the end of the season. We all have this great goal in mind, but for now, what counts is only Sunday."