Bilic has impressed since taking over the Hammers on a three-year deal last June, guiding the side to fifth in the Premier League standings with seven games left and through to the quarter-finals of the FA Cup.
Club joint-chairman David Sullivan said in the Mirror: "I will give Slaven a new deal in January.
"I just want to see that he is not a one-season wonder. I'm sure he is not, but we will talk next January - or at the end of next season.
"I have to tell you that he is interested in the project, not money.
"He stayed at Croatia on £2,000 a week for five years when he would have had bundles of offers. He is not really into money. He is more interested in getting the best players for the club than the best money for himself."