The Serbian has a year left on his contract at Lazio and is likely to move on from the Serie A giants in the ongoing transfer window.
He has been linked with a move to the Premier League, where West Ham, who will look to sign two midfielders if Declan Rice is sold, are considering taking him to the London Stadium.
But the player would prefer to stay in Italy even if he leaves Lazio and Juventus are pushing to grant him his wish.
According to Italian outlet Tutto Mercato, the Serie A giants have taken the lead in the race to sign the Serbia international.
He has emerged as a top target for Juventus and the club are growing increasingly optimistic about signing him.
Talks are ongoing between all the parties and Lazio are confident of closing out a deal to sign Milinkovic-Savic.
Lazio are ready to sell the midfielder due to his contract situation and want somewhere around €30m from his departure.
