The Premier League champions are in talks with Juventus and the club are confident a £44million deal can be agreed for the right-back.
Cancelo is keen on a switch to the Premier League and Manchester United have been credited with a transfer interest in the Portugal international.
But Goal claim Cancelo could be City’s first signing of the summer as they prepare to offload Danilo.
The Brazilian could take Cancelo’s place at Juventus, while Napoli’s Elseid Hysaj and Tottenham’s Kieran Trippier are also options for the Serie A champions.
City are in for another busy summer as Pep Guardiola targets a push for the Champions League next season.
Despite retaining the league title for the first time, City were dumped out of the Champions League by Tottenham in the quarter-final stages.
Guardiola wants to add a midfielder to his ranks this summer, with Atletico Madrid’s Rodri a major target.