Three straight Premier League defeats have led to rumours that joint-chairmen David Gold and David Sullivan are weighing up potential replacements for Bilic.
However the Croatian, who has another year on his contract, maintains he is only focused on getting back to winning ways, starting at Hull on Saturday.
"Nothing has changed in the last few days," he said. "What do you want me to say? There is nothing new I can say about it.
"I just concentrate on my job. I am totally focused on the next game. That (speculation) does not worry me. I am not reading it or making phone calls or whatever.
"We are in a position where we can have a good finish to the season. We have a lot of games to play and there is a lot to play for.
"I was saying the same when, for example, earlier in the season when we were talking about a new contract. I was not bothered then, when it was positive.
"Now after three defeats there is speculation. I have a game on Saturday."
Rafael Benitez, Jaap Stam and Roberto Mancini are among those being touted for the role should West Ham part with Bilic.
But he added: "That does not annoy me. There is something between being worried and annoyed.
"But my head is clear and I am totally motivated and focused.
"I've been here long enough to know what to do - over a year and a half - with an objective here and there is still a job to do and I have my contract.
"At the end of the day my contract is not running out. I have another year here."
Bilic has ruled Michail Antonio out of the Hull trip, but the winger could be fit to face Arsenal in midweek.
Skipper Mark Noble returns to the squad after missing the defeat by Leicester before the international break with a dead leg.
