The union was created in the heat of the Max Mosley political war in 2008, with McLaren team boss Whitmarsh then taking over from FOTA's first chairman, Luca di Montezemolo, at the end of 2009.
Since then, the group has fractured, with Ferrari, Red Bull, Toro Rosso, Sauber and HRT all no longer listed as members on the official FOTA website.
And in a report by Dieter Rencken and Mario Fritzsche on the German website motorsport-total.com, Whitmarsh announced it "would be good if, after three years, someone else takes over the role" now.
He said it will be up to the FOTA members to elect a new chairman. The FOTA website lists Lotus' Eric Boullier as the current vice-chairman.
And the media report said Ross Brawn is another candidate.
"I would support either," said Whitmarsh.