Whitmarsh underlined that at present there would be no restriction on Button finishing ahead of Hamilton in a grand prix, but that the door was open for such a move later in the year.
Button currently has 76 points, 31 behind Hamilton and 78 behind championship leader Fernando Alonso, after struggling to get to grips with this year's Pirelli tyres in the opening half of the season.
"There may well come a point [where Button would have to support Hamilton], but with nine races to go and 25 points per race things can change quite quickly," said Whitmarsh.
"We must be measured when we talk to the drivers about when they put their support behind another driver," he added.
Whitmarsh insisted that both drivers would have equal opportunity to win in Belgium this weekend and that McLaren would not be making a decision for a number of races, especially following Button's upturn in form in Germany and Hungary.
"I think the good news is that we go into Spa and both our drivers will be trying to win. Jenson has had some strong showings before the break and he is a very intelligent driver," he said.
"It would be quite a few races' time before we would look at the situation.
"Jenson is a winner. He and Lewis have a great relationship but Jenson will try to beat Lewis this weekend."