Although Hamilton's current McLaren deal runs out at the end of this year, and there remains a chance that Mercedes could lure him over if Michael Schumacher does not continue, Whitmarsh insists both team and driver are happy to bide their time to ensure what they agree on is best for both parties.
And ahead of what looks set to be a tight battle for the world championship over the second half of the campaign, Whitmarsh is convinced there will be no detrimental effect if nothing is sorted out before the Belgian Grand Prix.
"I honestly don't think it is an issue," Whitmarsh told AUTOSPORT. "You get a few questions over a weekend about it, and it is clearly fascinating to some people, but I really don't think it is an issue.
"Lewis and I have spoken two or three times at length. I think we are closer than we have ever been, and I have known him [Hamilton] since he was 11, and our conversations have been about how we are going to beat the other teams, and how we are going to try and win races. We don't talk about these issues at race tracks because I don't think it is the right environment.
"Ultimately it [the contract situation] is relatively straightforward. If Lewis wants to stay in the team, which he has told me he does, then he should do. And if we want to keep him, then we should do.
"If the answer to both those matters is yes, then I think it is eminently doable - so not something that has to have as much focus as turning up at races, trying to bring the quickest car you can and doing the best job possible."
Although Hamilton has had some frustrations this year, and lies 47 points behind championship leader Fernando Alonso, Whitmarsh thinks he is in the best form of his career.
"I think inevitably you can pick over the bones of issues in minutiae, and come to a conclusion, but if you stand back, I think anyone who has closely observed Lewis in terms of where he is in his head, where he is in his focus, and in his confidence - I think he is actually in a much stronger position now than he was last year," he said.
"He has gone through some interesting cycles, and it has been interesting for some of us who have known him for a good many years to see that. He is in a stronger place and, although it doesn't mean everything is going to go right for him, he is stronger mentally than he has ever been.
"He has had some big challenges, and last year by his extraordinarily high standards was not one of his better years. But he is a passionate driver who wants to win races, and I would be very worried if he did not exhibit those characteristics - and he is stronger minded and clearly more experienced than he has ever been."