The 23-year-old was a key player for Unai Emery's side, making 50 appearances in all competitions as they reached the Europa League final and finished fifth in the Premier League.
He is tied to the north London outfit for a further four years, but Milan are said to be preparing an offer for him as they look to reunite him with his former Sampdoria coach, Marco Giampaolo, who took the helm at San Siro this month.
The latest reports say they will offer Franck Kessie and Ricardo Rodriguez as part of the deal to land Torreira, who admitted a few weeks ago that he struggled to adapt to life in England because of the weather and language, saying: "I liked living in Italy more."
But he says he has not heard from the Italian outfit and is enjoying his time at Arsenal, suggesting he is set to stay put this summer.
"Today I’m in the Premier [League] and happy to be part of Arsenal. Adapting was not easy, but I only think about the team. I’m happy to be there."
Last week, Torreira's agent said there had been no approach from the Italian side, but said that a reunion with Giampaolo would be "special" for the player.
“I know nothing about the Rossoneri's interest, no one contacted me,” he said.
“I have learned of this possibility through the press.
“Could a call from Giampaolo be something special for Lucas? Yes, clearly.”
Torreira has previously expressed a desire to play for Boca Juniors, saying it has been his dream to represent the Argentine giants since childhood.