Sources close to both clubs have confirmed that the framework of a deal is being put in place as City prepare to sell Brazil international Danilo.
Danilo himself could also be an option, having come close to moving to Turin from Real Madrid before he eventually chose Manchester in 2017, but as things stand the two clubs are discussing a cash-only deal.
City have been prepared for Danilo's exit for several months and have been scouting the market for replacements. Crystal Palace right-back Aaron Wan-Bissaka is also on the Premier League champions' radar, although they would face stiff competition from Manchester United, who are keen to sign the 21-year-old.
Portugal right-back Cancelo is keen on the move but Juve are yet to sanction his sale, as they want in excess of €50m. City believe a transfer fee in that region is reasonable, although a final agreement is not yet in place.
Cancelo, 25, could become City's first signing of the summer, despite a long-held confidence that Atletico Madrid midfielder Rodri would join the club for €70m (£62m/$79m).
The Spain international is having second thoughts on the move and has publicly admitted that he has asked Atleti for "space and patience" to decide on his next move.
City have not given up hope of signing the 22-year-old, but have identified an alternative in case he eventually decides not to move to the Etihad Stadium. Marcos Llorente and Tanguy Ndombele have been linked, but Goal understands they are unlikely to be signed.
City are also interested in Leicester City's Harry Maguire, but the Midlands club are holding out for £75m ($95m), plus add-ons. That would make him the most expensive defender in history, and City are reluctant to pay such a fee.
The Blues' transfer priorities are a defensive midfielder and a centre-back, with Rodri and Maguire as top targets, with a new right-back and a new forward only coming in should current squad members leave.
Danilo, therefore, looks certain to leave the club, given City and Juve have held several rounds of meetings regarding Cancelo.