The Briton has been at the helm of the teams' body since the end of 2009, when he replaced Ferrari president Luca di Montezemolo.
Although the position was originally supposed to be occupied on a rotational basis for 12 months, Whitmarsh has been there for nearly three years.
But the McLaren boss has revealed he will not stand for re-election next time.
"I'm never going to volunteer for it," Whitmarsh told AUTOSPORT. "I think it's probably healthy, I suppose it's three years or whatever, I think it would be quite healthy for someone else to do it now. I think it's for the teams to decide on that.
"I care about Formula 1, whatever role I'm in. McLaren I think, has been an extraordinarily good citizen, in my opinion, of the sport.
"We [FOTA] have tried to be a galvanising, stabilising force, trying to understand the issues of all the players. Whatever happens, we'll continue to try and do those things. But I think it would be quite neat for someone else to have a go at it."
Whitmarsh said he has not spent time considering who may replace him, but he feels it would be a good chance for whoever takes over.
"I think it depends. I mean, it's a long way away. At the moment we've got 10 races left and I'll concentrate on that and on other things. We'll see what happens, but my recommendation to them will be that someone else does it. It'll be a good opportunity for them."
When asked if Mercedes boss Ross Brawn or Lotus chief Eric Boullier could be possible candidates to replace him, he said: "I'd support either of those candidates."