Speculation over Hamilton's McLaren contract, which ends after the current season, has been the subject of constant speculation this season.
However, Whitmarsh has insisted that Hamilton wants to stay and that a new deal could be close.
"If Lewis wants to stay in the team, which he has told me he does, then he should do," Whitmarsh said.
"Lewis and I have spoken two or three times at length. I think we are closer than we have ever been."
Hamilton has spent his entire Formula 1 career at McLaren.