The 20-year-old joined the Hammers from Charlton last summer but has only three Premier League appearances to his name after being sent out on loan at Huddersfield last season.
Poyet played in West Ham’s 3-0 victory over Andorra minnows FC Lusitans in their first Europa League qualifying round tie and could find more opportunities to press for a place as Bilic looks to lead his team through the group stages.
“My preference is to want to be at West Ham,” he said, when asked if another loan move may be on the cards.
“That is where I want to be and that is where I want to play. If the manager tells me ‘Look, you are better off going out on loan and getting some games’, then I will respect him for that and I will do that.
“But until I am told to leave, I am not going anywhere.
“If you are a young player and not playing, then as soon as there is a new manager, the thing you want to do is impress… get in his good books and then he trusts you.”
With the Europa League fixtures and the hope of further runs in the FA Cup and Capital One Cup, Poyet believes he and a number of other young players at the club could be given the opportunity to prove their worth.
“It depends how far we get in things like cups and Europa League,” the midfielder said of his chances of playing more regularly.
“He (Bilic) might give a chance to some of the young players. We were unfortunate last season as we lost the Capital One Cup against Sheffield United early on so it was difficult.
“Hopefully, fingers crossed, some youngsters will get the chance to play.”