Hamilton's title push had been compromised by multiple pitlane mistakes so far this season. The latest error cost the Brit pole position and resulted in the 27-year-old being demoted to the back of the grid for the Spanish Grand Prix.
Whitmarsh says that he is expecting to continue "working with him [Hamilton] for a long time to come".
When asked if he thought the team mistakes could affect Hamilton's contract situation, The Telegraph quotes him as saying: "No, I don't."
"He has got to build the support of the team, he has got to feel comfortable doing it, he has got to want to drive and he is in good shape. I look forward to working with him for a long time to come."
There are rumours that Hamilton could be scouted by Ferrari when Felipe Massa's deal with the side comes to an end.