The Serie A champions value Cancelo at around €55 million (£50m/$61m), but City will look to lower this sum by adding Danilo into the deal.
If such a swap deal does transpire, it could mean City would end up paying closer to €25 million (£23m/$28m) for the 25-year-old.
City were heavily linked with Cancelo at the beginning of the summer transfer window, with the Portugal international seen as an ideal addition in the full-back role.
That interest appeared to have cooled as right-back Kyle Walker signed a new five-year contract at the Etihad earlier in the summer, but Guardiola is now keen to add a third permanent signing of the window.
Cancelo joined Juventus from Valencia last summer after spending the previous year on loan at Inter, and made 34 appearances in all competitions last season. A technically proficient, attack-minded full-back, he would seem to fit the Pep Guardiola mold well.
With the Premier League transfer window closing on August 8, Paratici has a busy week ahead as he travelled to London on Thursday for talks surrounding the week’s other high-profile swap deal mooted in Manchester.
United’s desire to swap Romelu Lukaku for Dybala has emerged in recent days, though talks are still at an early stage. It has been reported that both clubs would be happy to go ahead with a deal, but it remains unclear whether Dybala would agree to swap Turin for Manchester.
The 25-year-old had a somewhat disappointing season for Juve last season, scoring just 10 goals in all competitions – a significant drop on the previous year’s total of 26.
Despite being signed as one of Serie A’s premier talents in 2015 and scoring 57 league goals since then, he is not thought to be in new manager Maurizio Sarri’s plans.