City's two-year European suspension has led to suggestions that a number of the club's players could look to leave the Etihad Stadium during this summer's transfer window.
According to Tuttosport, Juve are interested in signing Jesus, who is thought to be valued by the Premier League champions in the region of £58m.
The 22-year-old has scored 16 times in 33 appearances for Pep Guardiola's side during the 2019-20 campaign, including four goals in five Champions League outings.
The Brazil international has only started 12 Premier League matches during the current season, though, with Sergio Aguero still ahead of him in the pecking order at the club.
Jesus has a record of 61 goals and 25 assists in 133 appearances for the reigning English champions since arriving from Palmeiras in January 2017.