Biglia, 31, is under contract until June 2018, but is expected to leave Stadio Olimpico in the off-season.
"Lucas talked to Lazio a month ago, declaring his choice to leave Rome," Enzo Montepaone was quoted as saying by Il Messaggero.
"There's a deal with Milan and we're waiting for the two clubs to come to a definitive agreement.
"I know they're talking about finding a solution, because there's also an opportunity in England, but I can't say any more about that.
"Milan and Lazio are talking and they have to find a deal, next week I'll be in Italy and hopefully everything will be resolved quickly."