The Uruguayan arrived at the Emirates last summer from Sampdoria in a deal worth £25m.
Torreira enjoyed an impressive campaign in the heart of Arsenal’s midfield and he established himself as a fans’ favourite.
But the midfielder is reportedly unhappy in London and he sparked speculation around his future earlier this summer by announcing that he misses life in Italy.
According to Italian journalist Vito Angele, Arsenal are happy to sell Torreira.
The Gunners would demand at least €45m (£40m) to part with the 23-year-old.
Angele claims Torreira wants to join Milan but Arsenal will only let him leave if their terms are met.
Suggestions of an Emirates exit after just one season emerged following the star’s complaints about life in England.
“I don’t know if there are many things that I enjoy,” he said.
“I think it was better in Italy.”
Arsenal star Lucas Torreira
“I think it was better in Italy. England is a totally different world, a very large country.
“The language [barrier] has cost me, to be able to relate with my peers and with the people. It is very difficult when you can’t have dialogue.
“And so is the climate. You go out in the morning and it is cloudy, you arrive late to your home and it is cloudy.”
And his agent, Pablo Bentancur, fuelled speculation by admitting his client would like Milan to be interested.
When asked by Calciomercato if a call from Milan boss Marco Giampaolo would be special, he replied: “Yes, clearly.”
But he remained coy when asked for concrete details.
“I don’t know anything about the Rossoneri’s interest, no-one’s contacted me,” Bentancur continued.
“I learned about this possibility through the press.”