The Uruguay international has been training individually at London Colney after returning from his loan stint with Atletico Madrid.
Torreira is said to have expressed his desire to fight for a place in the Arsenal team, but was told he does not have a place in Mikel Arteta’s plans for the season.
With the 25-year-old not having a place in Arteta’s plans for the season, a return to Italy has been said to be the most likely option for him.
Torreira has been linked with a move to Serie A club Lazio this summer, but it has emerged that he is close to joining Fiorentina.
The former Sampdoria midfielder is set to join La Viola on a season-long loan deal despite initial suggestions that it could be a loan with an obligation to buy.
Torreira is set to travel to Italy on Tuesday as he edges closer to a temporary move to Fiorentina.
The former Serie A star, who joined Arsenal from Sampdoria in the summer of 2018, has two more years remaining on his contract with the Gunners.