Last month, it was claimed that Juve were considering a £58m move for the Brazil international, who has found the back of the net on 18 occasions in 37 appearances during the 2019-20 campaign.
According to Metro, the Italian champions have recently stepped up their interest in the South American having sent a scout to watch him in action against West Ham United in February.
The report claims that the 22-year-old's movement against the Hammers impressed the Old Lady, who are looking for a more mobile forward to replace Gonzalo Higuain in the starting XI.
Jesus has largely played second fiddle to Sergio Aguero at the Etihad Stadium this season, although the Brazilian was handed a start against Real Madrid on February 26 and found the back of the net as Pep Guardiola's side claimed a 2-1 advantage in the first leg of their last-16 Champions League tie.
The former Palmeiras youngster has a contract in Manchester until the summer of 2023.