Poyet joined the Hammers from London rivals Charlton Athletic in the summer of 2014.
The 20-year-old played on loan for Championship outfit Huddersfield Town for a short spell during the 2014-15 campaign.
The Uruguay Under-20 international could make just three Premier League appearances for West Ham, creating one chance and having a pass accuracy of 91% in the process.
Poyet has said that he is looking to impress Bilic during pre-season and also hopes to play in the Europa League qualifiers.
“People can impress in training but there’s nothing like impressing with what you can do in games,” the youngster told West Ham’s official website.
“That’s what matters, so it’s an opportunity for everyone, the club and the fans to travel to Europe. It’s a chance to play against some of the big clubs in Europe.”
When asked about his personal targets for the 2015-16 campaign, Poyet said: “Targets? I’ll have to see.
“I haven’t worked with the manager, I know things about him and have watched how his teams play, but he’ll speak to the players and then we’ll start to see the differences from the previous manager. It’s all very exciting and new for everyone and it’s a good time to be at the club.”
West Ham will be taking the Europa League seriously, but one suspects that new manager Bilic will give chances to youngsters.
Poyet is a talented young player who can only improve and develop if he is given regular first-team chances.
It will not be easy for the Uruguayan, though, which means that he has to make the most of the chances he will be offered initially.