Fabianski played down a move to Italy, saying he's happy playing in the Premier League.
Fabianski was signed on a free transfer last summer after his contract had run out at Arsenal, and has proved to be a worthy number one by keeping Gerhard Tremmel out of the side, after Michel Vorm departed in the summer.
The Polish goalkeeper is quoted, saying: "My brother mentioned that this information (about interest from Roma) appeared in newspapers, but to be honest, I feel very good in the Premier League.
"I know the language and culture. I think that the Premier League — despite the failure of English teams in European competitions this season — is still the most attractive place to play.
"That's why I'd rather not move anywhere."
It will certainly be a boost to Garry Monk as he wouldn't have wanted to have to make another big change at the back of what seems to be a pretty solid defensive unit the Swans currently possess.
Having not really got a look-in on a regular basis at Arsenal - despite playing a big part in their FA Cup success last season - Fabianski has shown he can be an effective number one goalkeeper for a promising looking Premier League side.
He has managed to keep 11 clean sheets for the side this season - with only Southampton's Fraser Forster having kept more this season. With the Saints keeper unfortunately sidelined for the rest of the season because of a broken kneecap, Fabianski could end up with the golden glove in his first season at the Liberty Stadium.