Madrid are widely regarded as the favourites to sign the France international, who has scored nine times in 11 appearances for PSG during the 2019-20 campaign.
However, according to Tuttosport, Juve are preparing to launch 'Operation Mbappe' in the hope of securing a deal for one of the leading youngsters in world football.
The former Monaco youngster played a key role in France winning the 2018 World Cup when he was just a teenager, while he has managed 69 goals in 98 appearances for his current club in all competitions.
Mbappe's current deal in Paris will expire at the the end of the 2021-22 campaign, and the 20-year-old will reportedly not be signing a new contract in the French capital.
Juve continue to dominate in the Italian league - winning each of the last eight championships - but the Old Lady have not enjoyed European success since the 1995-96 campaign.