Speculation has grown that Milan have stolen a march in the pursuit of the player, however, with reports on Wednesday claiming that a double deal for Keita and midfielder Lucas Biglia had been reached between the clubs.
Roberto Calenda, Keita's agent, has now confirmed that Lazio have informed him that a deal with Milan has been reached.
"After a few months apart, we met with the president [Claudio Lotito]," he told told Sky Sport Italia.
"They communicated to us that they have reached an agreement with Milan, so we realised that he is on the market. Now we will assess our options.
"It's difficult to know what the price is when it comes to Lazio. We talked about many things with Claudio Lotito, but there has never been a concrete offer of a renewal."
Keita's contract reportedly has only one year left to run, prompting speculation that Lazio would be forced to sell in the next transfer window to avoid losing him for free in 2018.
Juve general director Giuseppe Marotta claimed last month that they were keeping a close watch on the forward with a view to making a bid.
"We are keeping an eye on his situation and are interested, but we are calm," he told Radio Anch'io.
"We are always looking for talents who could play alongside our more experienced players."
Keita registered 16 goals and six assists in all competitions last season, helping Lazio to a fifth-place finish in Serie A and the Coppa Italia final, where they lost to Juve.
Milan have been active in the close-season as they look to bolster their squad in the hopes of challenging for a Champions League spot next term.
The signing of Ricardo Rodriguez from Wolfsburg was confirmed on Thursday, while Mateo Musacchio and Franck Kessie have already completed moves.