Juventus and Spurs are also interested in the player though Chelsea have shown serious interest by scouting him thoroughly.
Blues boss Antonio Conte is eager to add another wing-back to his ranks before the end of the transfer window.
The Premier League champions have been trying to land Juventus star Alex Sandro for several months but have failed to reach a breakthrough over the potential deal.
A move for Sandro now appears off and Conte is looking at other targets with Valencia ace Cancelo on his radar.
Chelsea are said to have scouted the 23-year-old Portugal international at this summer’s Euro Under-21 tournament and have been impressed by his performances.
Sky Sports reporter Kaveh Solhekol said: “Conte wants to sign at least one wing-back this summer and one of the players he is interested in is Joao Cancelo.
“He’s a Valencia right-back who was scouted playing for Portugal at the European Under-21 Championships.
“And he’s been watched again during pre-season.
“Juventus and Spurs are also said to be interested. He’s valued at about £25m.”
Meanwhile, Chelsea are one of several clubs being linked with Paris St-Germain right-back Serge Aurier.
The 24-year-old is open to a move away from Paris but issues with his visa could mean the Ivory Coast international is forced to stay put.
Solhekol added: “Another wing-back Chelsea are interested in is Serge Aurier, he is at PSG. He lost his place there because of new right-back Dani Alves.
“This deal would be pretty complicated, because Aurier is appealing against an assault conviction that means he cannot enter the UK at the moment.”