This is according to talkSPORT, who also claim that Manchester City - who won their second Premier League title in three years at the weekend with a simple 2-0 win over West Ham - are also chasing the Portuguese starlet.
19-year-old Cancelo - a regular at youth level for his country - joined current club Benfica back in 2008, progressing through the youth ranks at the Estadio da Luz.
A regular for Benfica B over recent seasons, versatile full-back Cancelo was handed his full first-team debut on Saturday as Jorge Jesus' side rounded off their title-winning 2013/14 Primeira Liga campaign with a disappointing 2-1 defeat to rivals Porto.
While you wouldn't anticipate that Cancelo would be ready for regular Premier League action straightaway, it would certainly come as no shock whatsoever to learn that Chelsea and Liverpool were pondering the addition of a new full-back.
With Ashley Cole out of contract this summer and Luke Shaw being linked heavily with an imminent switch to Manchester United, Chelsea boss Jose Mourinho - whose first season back in the dugout at Stamford Bridge has ended without a trophy - would perhaps be wise to investigate other options.
Liverpool, meanwhile, evidently have a rather pressing need for a new left-back, with first-choice Jose Enrique having missed most of the season with a knee problem that left the Spaniard requiring surgery.
While right-back Jon Flanagan has looked capable of filling the void on a temporary basis, it is unlikely that he will be asked to remain their for the long-term.
Liverpool did complete the loan signing of Aly Cissokho during last summer's transfer window, of course, but it seems likely that the Frenchman will now return to Valencia after a disappointing spell at Anfield.