The 25-year-old has fallen down the pecking order since the arrival of Gunners boss Mikel Arteta and is now considered surplus to requirements.
According to Corriere Dello Sport, La Viola are keen to sign a central midfielder and Torreira is one of three names on their shortlist, along with Inter Milan's Stefano Sensi and FC Koln's Ellyes Skhiri.
Fiorentina are yet to enter negotiations with the Gunners, though they are expected to make a move in the coming weeks as Torreira is their primary target.
The Uruguayan international, who joined Arsenal from Italian side Sampdoria in 2018 for a deal worth around £26m, has made 89 appearances for the north London club and was part of the squad who lifted the FA Cup in August 2020.
Torreira spent last season on loan with La Liga champions Atletico Madrid, making 19 league appearances, though just three of those outings were from the start. body check tags ::