Torreira was sent out on loan to the Viola last summer after falling out of favor with manager Mikel Arteta.
The midfielder has reportedly impressed head coach Vincenzo Italiano, who wants to sign him on a permanent basis, according to La Nazione.
The Serie A club is willing to pay €15 million (£13 million) for the Uruguayan, who will be given a four-year contract.
According to the same report, Fiorentina ‘will enforce’ the right to buy for the 25-year-old, whose career has been resurrected at the Artemio Franchi, ‘barring surprises.’
Last year, the Uruguayan was sent out on loan to Atletico Madrid after being left out of Arteta’s plans.
However, that trade did not pan out, and the Gunners quickly offloaded him to Fiorentina.
With 17 Serie A appearances under his belt, Torreira has established himself as a starter in Florence.
He joined Arsenal in 2018 from Sampdoria and has made 89 appearances in all competitions.
Torreira made an impression at the Emirates under former boss Unai Emery, but he was unable to overcome Arteta.
Previously, the Spanish head coach stated: “Lucas has a big heart and gives his all to whatever he does.
“That’s why he’s not one of those players who enjoys waiting for his turn on the bench.
“On the pitch, he needs to prove what he can do.” He’s having fun with the game. That’s exactly what happened at Arsenal.
“Lucas is sincere and wants to leave his heart on the field, but that is determined by the coaches, and he didn’t matter to the current Arsenal boss.”