Arsenal want to offload Torreira on a permanent basis at the end of the season and Fiorentina have the option to sign him for around £12.5million.
The 26-year-old Uruguayan has done well in Italy this season as part of a Fiorentina team that are making a surprise challenge for Champions League qualification.
But Torreira has no future at Arsenal under Mikel Arteta and the Gunners are willing to take a significant loss on the £25m they paid to sign him from Sampdoria in 2018.
Arteta agreed to let him leave last summer after spending last season with Atletico Madrid.
The Uruguayan had been keen on a move to Boca Juniors, but the Argentine club did not have the financial power to firm up their interest.
Fiorentina eventually made a move for Torreira and he is once again enjoying his football back in Italy.
Torreira had arguably the best spell of his career when playing in Serie A for Sampdoria.