Torreira left Sampdoria to join the Gunners last summer, making a total of 31 starts and 18 substitute appearances during his debut campaign.
However, the 23-year-old revealed earlier this week that he had struggled to adapt to life in England, acknowledging that he preferred his time in Italy.
According to Gazzetta dello Sport, that has resulted in Milan looking to take advantage of the situation by lodging a formal bid for the Uruguay international.
The report adds that Milan’s chief operating officer Zvonimir Boban and sporting strategy and development director Paolo Maldini are ready to make a sustained assault on trying to sign the player.
Arsenal are said to be eager to keep Torreira at the Emirates Stadium, despite the possibility of being able to make a quick profit on the tough-tackling midfielder.