The 24-year old, who joined the East Londoners permanently last summer after a year on loan, is believed to be on the radar of Liverpool should Philippe Coutinho depart the club.
However, Bilic insists that the Argentine is settled at the London Stadium and is focused on returning to full fitness for the new Premier League season.
"With Manuel... no player is bigger than the club," Bilic was quoted as saying by Football London at a press conference held on Friday. "I don't mean contracts, just one player, he is part of the team like any other player. He is one of our key players, a great lad and he knows his situation.
"I spoke with him last season, at the end of the season, then in the beginning of pre-season. He knows we are looking after him and that he has a big year ahead of him. We know his situation and we will do everything possible to sort him out.
"He has a long contract already, but the owner and chairman always appreciate those situations and I know the chairman activated his clause well before, last time, than he could have done. No doubt he is a key player.
"That's what I am talking about. He never showed me, any sort of things that he is unhappy. Then of course, every players wants to use their situation in the best possible way but I know for sure that he is happy here."
Lanzini joined West Ham initially on a season-long loan from Abu Dhabi club Al Jazira in 2015, having started his career at River Plate and then Fluminense.