The 18-year-old midfielder – son of Sunderland manager Gus – has only made a handful of appearances for the Addicks so far, but he is already being dubbed as a potential future star.
Tottenham and Southampton have been linked with early moves for his signature, and now it has emerged that the Hammers are also in the battle.
Poyet has been commended for his technically adept style, with the Spanish-born teenager’s fledgling displays having helped the London club to the FA Cup quarter-finals.
It is understood that the youngster is keen to move up to the top tier, an opportunity Sam Allardyce may offer him this summer.
The West Ham boss is said to have been watching Poyet closely, and now that relegation fears have eased a little plans for the coming transfer window have been ramped up at Upton Park.
Charlton are aware of interest in their man, and may be hopeful that a bidding war will drive up his price.
Gus also had a successful career in the Premier League, representing Chelsea and Tottenham between 1997 and 2004.