He said a company called Wheelabrator Technologies Incorporated had been short-listed as a preferred bidder but the decision would have to be backed by the five councils involved.
The result will be presented to the Norfolk County Council cabinet next week, when councillors will decide whether to sign a contract with Cory Wheelabrator to build the plant.
"This is despite the fact that 42% of people in the borough and 74% in Norfolk overall (including King's Lynn) state that Energy from Waste incineration is their preferred option after recycling, " a spokeswoman for Cory Wheelabrator said.