Torreira is considered surplus to requirements at Arsenal and was left out of the club’s Carabao Cup victory against Leicester City, despite showing plenty of early promise after joining the Gunners from Sampdoria for around £26.5m in 2018.
Head coach Mikel Arteta is keen to sell both Torreira and Matteo Guendouzi in order to extend Arsenal’s budget and launch a bid for either Atletico’s Thomas Partey or Lyon’s Houssem Aouar.
Atletico are yet to make a formal bid for Torreira as they first need to sell Mexican midfielder Hector Herrera, who made 30 appearances last season and attracted interest from West Ham in January.
Herrera, 30, chose to stay in Spain and fight for his place under Diego Simeone, with the Hammers instead turning to Slavia Prague midfielder Tomas Soucek, who has impressed since making the move to east London.
Torino are interested in signing Torreira on loan initially, while Fiorentina have seemingly ended their interest in the 24-year-old after failing to make a breakthrough in negotiations with Arsenal, who are hoping to recoup around £20m.
Asked about Torreira’s absence, Arteta said: “I am not making decisions because players might leave or stay, it is just for the players we see every day who are in the best possible condition to compete and get us closer to winning football matches.”