Torreira only arrived at the Emirates last season, and Milan are said to want to bring the Uruguayan to Serie A as they begin a new era following the departure of Gennaro Gattuso as manager.
According to Gazzetta dello Sport, Torreira and his girlfriend are already fed up with life in England and Milan want to take advantage.
Lucas Torreira, pictured on Uruguay duty last week, is said to be unhappy living in London
The Arsenal midfielder is ‘wanted by AC Milan’, who are keen to bring him back to Serie A
The front page of Gazzetta dello Sport details AC Milan’s swoop for Torreira this summer
The paper report that Chief Operating Officer Zvonimir Boban and Sporting Strategy and Development Director Paolo Maldini are ‘officially at work’ to begin the siege for both Torreira, and also Liverpool defender Dejan Lovren.
Arsenal, meanwhile, are understood to be desperate to keep hold of the player, who will likely be a huge part of Unai Emery’s plans going into next season.
Torreira’s partner is from Genoa and is said to be very keen on a move back home rather than remaining in London for another year.
The midfielder also recently threw his future into doubt after suggesting his life ‘was better in Italy’.
He has been a mainstay in the midfield since Unai Emery took charge alongside Granit Xhaka but talk of a departure after just one season will concern his manager.
Torreira told Uruguayan outlet Ovacion : ‘I don’t know if there are many things that I enjoy (in England). I think it was better in Italy. England is a totally different world, a very large country.
‘The language [barrier] has stopped me, to be able to relate with my team-mates and with the people. It is very difficult when you can’t have dialogue.’
Torreira (right) chats to Luis Suarez (left) and Cristhian Stuani during Uruguay training
AC Milan chiefs Zvonimir Boban and Paolo Maldini (pictured) are ‘at work’ to get Torreira