The Gunners are reportedly determined to hold out for £45m on a player they signed just last summer, according to La Gazzetta dello Sport.
But, Tuttosport report, there is increasing confidence from Milan’s owners Elliott Management that Arsenal could sell Torreira for £35m or less.
AC Milan ‘are prepared to offer Arsenal £35m for their Uruguayan midfielder Lucas Torreira’
Torreira only signed for the Gunners a year ago and helped them reach the Europa League final
It would see the Uruguayan reunited with his former coach at Sampdoria, Marco Giampaolo, who has just been appointed by the Rossoneri.
Torreira, 23, played 50 times during his first season with Arsenal after signing for £26m from Sampdoria and helped them reach the final of the Europa League.
However, he has admitted struggling to adapt to the English lifestyle, language and climate, while his girlfriend, Vittoria Repetto, who hails from Genoa, is reportedly not happy in London.
Giampaolo is keen to make Torreira a Milan player and this could offer a solution though Arsenal would naturally be reluctant to sell him.
Speaking ahead of the Copa America, where he is in action with Uruguay, Torreira was asked what he enjoys most about England.
Marco Giampaolo has just been appointed Milan manager having previously coached Torreira’s former club, Sampdoria
Torreira, left, in action for Uruguay during their Copa America fixture against Japan
He said: ‘I don’t know if there are many things that I enjoy. 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’s 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.
‘It is strange a little bit, the sun, the more of us that we are here and we are accustomed to having always or almost always the sun.
‘But as the years pass, I’m going to be adapting.’