Camacho, who is described as one of Portugal's brightest prospects in his age group, arrived at City two summers ago from Sporting Clube de Portugal.
However, the report claims the 15-year-old has been informed he is unlikely to earn a professional contract at the Etihad Stadium.
And that has alerted Liverpool, who have a long-standing interest in Camacho, with talks now at an advanced stage, according to ESPN.
The attacking midfielder can play on either flank, as well as through the middle, and is of Angolan descent.
However, he's already been capped by Portugal at under-16 level, scoring three goals in five appearances.
Should the deal go ahead, it would represent Liverpool's second raid on their North West rivals in quick succession, after the reported capture of right-back Diego Lattie last month.
In his seven months in charge of the Reds, Jurgen Klopp has already shown a willingness to utilise the young talents at his disposal - notably Kevin Stewart, Brad Smith and Sheyi Ojo.