Reports in Italy claim the 24-year-old is on the verge of a move to La Viola, with the deal including a £7 million loan fee and a £14 million obligation to buy next summer.
Torreira starred for the Gunners last season after joining from Sampdoria, but he endured a tough second term in England as he fell out of favour under Arteta, starting just two of the final 14 games of the campaign.
The Uruguayan follows Henrikh Mkhitaryan out of the Emirates exit door after he joined fellow Serie A side Roma on a free transfer.
Sokratis is also expected to move to Italy and join Napoli, while Sead Kolasinac is on the radar of Roma and former club Schalke as Arteta looks to boost his transfer budget and trim his squad.
There could be further exits too, with Rob Holding reportedly set to join Newcastle United on loan, while PSG, Juventus and Bayern Munich all hold an interest in Hector Bellerin.
The Gunners do look set to add though, with Dani Ceballos on the verge of rejoining on loan for the season, Thomas Partey still a priority midfield target and Houssem Aouar also on the club's radar.