The Daily Mirror has suggested that Cresswell is a target for Manchester City and Liverpool ahead of the summer transfer window.
However, Bilic is convinced that the former Ipswich Town man will remain with his side for the foreseeable future.
“He’s having a great season,” Bilic said. “Last year, he was Hammer of the Year. First of all, he’s a great professional and it’s a privilege to have those kind of players.
“He has improved a lot. On the ball, with his crosses and technique he was always good and he is almost like a playmaker on the left side, but defensively, he has improved tremendously and he has become a great player and a great full-back.
“Of course, that attracts interest of so many clubs, but I spoke to him, and first of all he’s under contract, and secondly, he is really happy here and he loves it here. He can’t wait for the new season. He is going to stay with us for a long time, hopefully.”
Cresswell has been a key player for West Ham so far this season, and he has put in a number of consistently impressive performances.
The 26-year-old may not have taken as many headlines as some of his teammates this term, but he has still been very reliable.
Cresswell has made 43 appearances for the Hammers this campaign, and he has firmly established his place in the London side’s first choice left-back.
Cresswell’s next chance to impress is likely to come in West Ham’s match against West Bromwich Albion on Saturday.
If the Hammers are able to win the match they could close the gap on fourth placed Arsenal to four points.