Andy Carroll is targeting a place in Roy Hodgson's squad for Euro 2016, and hopes to achieve it by helping West Ham secure European football.
Sunderland, and Carroll's former club Newcastle, have been linked with moves for the 27-year-old striker, amid reports the Hammers were considering cashing in on a player with a bad injury record.
But Bilic has no intention of getting rid of Carroll, who has looked back to his best recently and scored two goals in his last two matches.
"The club are not willing to listen to offers," Bilic said. "We want Andy to stay and perform like he does in most games.
"Nobody at the club wants to sell him, he's a very good player. But whenever he scores a couple of goals the rumours start.
"The only way he can stop the rumours is to play badly, which we don't want him to do.
"We don't want to sell him. He's very good in the dressing room and I know he's happy here."