Cresswell has reportedly attracted interest from Anfield, where he began his career as a youth player before being released and moving on to Tranmere and then Ipswich.
The 26-year-old has been a virtual ever-present since arriving at Upton Park in July 2014 and has even been touted for a potential England call-up.
But Hammers boss Bilic insists Cresswell has told him he wants to stay with the club ahead of the move to the Olympic Stadium next season and beyond.
"He is having a great season," said Bilic
"First of all he is a great professional, it's a privilege to have a player who is always available.
"Last year he was our player of the year
He played every game last year, this year I think he's missed one.
"He's improved a lot
With the ball, and on the ball with crosses and his technique, he's almost a playmaker on the left side of the pitch.
"But defensively he has improved so he became a great full-back and a complete footballer
He gets the interest of so many big clubs.
"I spoke to him
First he is under contract
Second, more important than the length of the contract, is that he is really happy here, he loves it here and he can't wait for the new season and all that hype.
"Those clubs can try to talk to him but I spoke to him a couple of times, he is very happy and he is going to stay with us for a long time
"
Cresswell will be in the Hammers side which travels to West Brom on Saturday looking to cement their place in the top six and qualify for Europe.
Bilic has a fully-fit squad available for the trip to The Hawthorns.
Source : PA
Source: PA