The team's managing director Jonathan Neale said last week the 2008 world champion is "close" to agreeing a new contract.
And boss Martin Whitmarsh has now been quoted as saying Hamilton, 27, "has told me" he wants to stay at the Woking based team.
"If Lewis wants to stay in the team, which he has told me he does, then he should do," Whitmarsh is quoted by the BBC and the Independent newspaper.
"Lewis and I have spoken two or three times at length. I think we are closer than we have ever been," he added.