The 19-year-old took in a temporary spell Huddersfield Town earlier in the campaign, but insists that a move to another Football League club holds no appeal at present - even if he isn't getting many starting opportunities at the Boleyn Ground.
West Ham possess masses of quality in central midfield this season, but Poyet is happy fighting for his place at the Hammers.
"I'm not one of those who is calling my agent all the time to find out what is happening and ask[ing] if anything is going on," he said.
"I'm only 19 and there are a lot of quality players in front of me but I'll just keep training and be prepared when I get my chance."
Poyet has been identified as one of West Ham's stars of the future and his relaxed attitude on receiving regular first-team football is likely to be due to the fact that he still has time on his side.
The teenager will feel that he can still develop from training with the high-class players in West Ham's first-team ranks this season.
Learning off players such as Alex Song can only benefit Poyet's career and it may be that sticking around and playing for the development side serves him well in the future.
However, despite his current apathy to getting game-time, there will come a time that Poyet needs to make the break through from fringe player to first-team starter and Sam Allardyce will need to ensure that he is thoroughly prepared for that moment when it does arrive.