At present the FIA are lenient with repeat offenders, with a driver incurring a 10-place grid penalty should he receive three reprimands over the course of a season.
One exception this year saw Lotus' Romain Grosjean handed a one-race ban for repeat incidents, with the defining moment when he took out three other cars in a first-corner smash in the Belgian Grand Prix.
Given the high-profile nature of what unfolded with Grosjean, Whiting is now considering applying points to a drivers' superlicence for a range of offences, similar to a normal road licence.
When a driver hits a particular tally, that would then trigger a one-race suspension.
Whiting, who is planning to broach the idea with the teams in Brazil next week, said: "We would like to see a system similar to the sort of thing you have with your road licence where you will accumulate points on your superlicence.
"If you get to 12 points, or whatever, you will have a race ban.
"You will accrue points for all sorts of penalties, whereas at the moment we have only got three reprimands, and two of those have to be for driving infringements.
"At the moment if you had a reprimand for being late for a press conference and a reprimand for being late for a drivers' parade, that wouldn't lead to a 10-place grid penalty.
"It has got to be for driving infringements, so if we looked at the superlicence approach where you get a point for this, two for that, it would all count."
Whiting suggested there would likely be opposition from the teams, but Whitmarsh feels as long as it is implemented correctly, he does not believe it will meet with much resistance.
"At the moment you have the three-reprimand system and you are punished, so I think this is presumably a further elaboration on that," said Whitmarsh.
"Like all things, any penalty system, providing it is administered in a correct and consistent manner, then why should we have any problem with it.
"It's the same for all the drivers and the same for all the teams."