Bernardeschi, 23, helped Italy Under-21s to reach the semi-finals of the Under-21 European Championships this summer.
The attacker entered that tournament off the back of a 14-goal season with Fiorentina, but he is currently refusing to sign a new deal with Viola.
Bernardeschi's current contract with his Italian club will expire next summer, and it has been reported that Manchester United are considering a move for the attacker ahead of the 2017-18 campaign.
However, according to Corriere dello Sport, Juventus currently lead the race, and the Italian champions will offer £34.6m, in addition to either Stefano Sturaro or Tomas Rincon, in a bid to secure Bernardeschi's signature this summer.
Bayern Munich, Chelsea and Paris Saint-Germain are also said to have a long-standing interest in the Italian.