The 27-year-old's deal runs out at the end of the season, and he has been linked with a move to Mercedes should Michael Schumacher not be retained by the German marque.
Hamilton hauled himself back into title contention with victory in Hungary before the current summer break, and Whitmarsh insists his contract situation will not be a distraction if a deal is not agreed before next weekend's Belgian Grand Prix at Spa.
Whitmarsh, who Hamilton has assured he wants to remain with the team, 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 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."