The Uruguayan enjoyed a solid start to life in north London but has struggled to make an impact since Unai Emery left the club.
Fiorentina, Roma, Torino and Sampdoria have all been tentatively linked with a move for Torreira this summer.
And Italian outlet Tuttosport reports the player's relationship with Arteta has fizzled out, meaning a move away from the Emirates now seems inevitable.
Torino boss Marco Giampaolo is said to have already spoken to Torreira ‘several times’, and Torreira has indicated he would make the move and reunite with the manager he worked with at Sampdoria.
Giampaolo’s brother Federico has even confirmed the interest.
“Taking Torreira will be very difficult because it is an operation that involves a great outlay from the club,” he told Tuttosport.
“And it is a negotiation unrelated to the simple will of the player, so many factors come into play. But in football, you never know.
“Maybe Marco convinces him, and Vagnati gets a yes from Arsenal: everyone in Turin wishes him well.
"It is a city that lives on football and Torreira can ignite enthusiasm like few other players.”
It comes as the Uruguayan has given his own take on his future earlier this year, telling Sport 890: “I have to think thoroughly about my future. I have a contract with Arsenal and I have to respect it.
“Obviously, if I were to leave, I would do it for the best possible destination. We have to be calm and wait.
“Last season I played continuously, this one less so.
“This year has been more complicated: I have lost continuity and confidence. I do not like this. At this age I need to play to be called up for the national team.
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“Transfer rumours? I don’t know anything right now. I need to rest because it was a very long season, I got injured, then there was the coronavirus.
“I have a contract with Arsenal, but if I have to change in the future it will be a decision I make for my own good.
“Every player looks for a team where he feels important. We will see what happens in the future.”