Pep Guardiola is keen on a move for the 25-year-old right-back amid uncertainty over Danilo’s future at the Etihad.
Cancelo, who helped Juventus win Serie A last season in his first campaign at the club, would like to move to the Premier League with Manchester United also having been credited with an interest previously.
But, according to Goal, City have been in advanced talks with Juventus over a move for the Portugal international, with the Italian giants understood to be looking for £53.6m before they allow him to leave.
According to the publication, further discussions between representatives of both clubs took place on Monday, with City taking a step closer to completing a deal after indicating that they are willing to increase their initial offer.
And the two sides are thought to be hopeful of agreeing a transfer fee of £44.7m plus add-ons.
Cancelo made 34 appearances for Juventus last season after joining from Valencia last summer.
It is believed that the arrival of Cancelo could bring an end to Danilo’s time with Manchester City.
Since his arrival from Real Madrid in 2017, the Brazilian has struggled to establish himself as a regular in Guardiola’s starting line-up.
Despite winning the domestic treble last season, Guardiola wants to mount another challenge on all fronts next time around.
That means more reinforcements in key areas, with central midfield also a priority, along with full-back.
Atletico Madrid midfielder Rodri is a major target for the club, it is believed.
City are also interested in Leicester City’s Harry Maguire, but the Foxes are holding out for £75m plus add-ons for the centre-half.
That would make him the most expensive defender in history and City are thought to be unwilling to pay that amount.
Meanwhile, the newly-crowned Premier League champions are close to reaching an agreement with Kyle Walker over a two-year contract extension at the Etihad.
The 29-year-old right-back has three years to run on the deal he signed when moving from Tottenham two summers ago, but the Blues are keen to retain the services of the England international for an additional two years.
Walker will be 34 by the time his proposed extension expires in 2024, with the former Sheffield United man poised become the fourth player to sign a contract lasting at least five more years alongside Aymeric Laporte, Ederson, Bernardo Silva, and Phil Foden.
City will be hoping to get their transfer and contrast business concluded early this summer so that they can concentrate on their preparations to win a third Premier League title on the bounce.