The Polish 'keeper is likely to be number two behind Petr Cech next season.
The Polish ‘keeper is currently on a season long deal with the Serie A side, having found himself further down the pecking order at the Emirates this season.
That is as a result of the arrival of Petr Cech, who was signed from rivals Chelsea in the summer and has since made the number one spot his own.
He was in impressive form again on Sunday with a series of impressive saves in the 0-0 draw with Stoke City, with many believing he is the factor that has turned Arsenal into title contenders this season.
He is extremely unlikely to lose his number one status next season, and Roma are keen to take advantage by securing Szczesny on loan for a second successive season.
The Italians are confident they can persuade the Frenchman to change his mind though, with negotiations between the two clubs thought to be frequent and cordial at this moment in time.