Milan boss Marco Giampaolo wanted to reunite with the Uruguayan, who he managed at Sampdoria.
And Torreira's agent Pablo Bentancur told TMW: "There was the possibility. Giampaolo is in the heart of Lucas.
"But Arsenal said he had no intention of selling the boy. Lucas is fine, the club are happy with him.
"This will be the year of consecration. With the Arsenal shirt.
"Milan is Milan, it will always be an important team, even if today it has some economic problems."