The 19-year-old son of Gus Poyet has made four appearances for the Hammers since his summer move from Championship side Charlton, with the latest coming in the 1-1 draw with Everton in the FA Cup on Tuesday.
He had already enjoyed a loan spell with Huddersfield Town earlier in the campaign, and he holds a promising reputation in the game having made 20 appearances during his debut season with the Addicks, being named as their Player of the Year despite only making his first appearance in January 2014.
The potential switch is being reported by the Daily Mail, and it is said that Huddersfield are also keen on bringing the young midfielder back to the John Smith’s Stadium for the second half of the campaign.
Despite turning out in the FA Cup third round fixture, it is reported that West Ham are keen on the deal going through, with the club keen on Poyet receiving consistent competitive match action as he continues to develop.
A defensive-minded midfielder, Poyet would likely be the replacement for Keith Andrews in the Hornets squad, who has been cast out of the first-team squad by head coach Slavisa Jokanovic, with his loan from Bolton likely to be terminated in the coming weeks.
Although he may be tempted to return to the Terriers, having already played for them this term, a switch to Watford allows only a short move to Hertfordshire from East London, and he will likely be a consistent fixture in the first-team of a side fighting for promotion to the Premier League.