Following the safety issues that came to light when Fernando Alonso gave Mark Webber a lift back to the pits after the Singapore Grand Prix, sources have indicated that the governing body is now reviewing the matter.
Alonso and Webber were both reprimanded for separate breaches of the rules, but these did not relate to the actual drive back to the pits.
Alonso was punished for breaking article 30.13 of the sporting regulations, which relates to cars being "driven unnecessarily slowly, erratically or in a manner which could be deemed potentially dangerous to other drivers or any other person".
Webber's reprimand was for breaching article 30.9 (b), which only allows drivers to be on the track if they have first received permission from a marshal.
AUTOSPORT has learned that Webber did not have permission to run on to the track, and he was specifically instructed by the marshals not to do so.
The spotlight on the incident means that the matter will be discussed at the next F1 drivers' briefing in Korea in a fortnight.
Although there are no plans to introduce a regulation that bans such 'taxi rides', which are not strictly outlawed, AUTOSPORT understands that the FIA is keen to impose a safety clampdown.
Drivers are set to be recommended not to risk future punishments for offering such lifts.
The FIA is to remind drivers that under no circumstances are they allowed to run on to the track without marshals' permission, nor should they stop to pick someone up in the manner that Alonso did.
The imposition of those instructions will effectively end the practice of such passenger rides, as drivers will not be allowed on track while cars are around to pick them up.
Collecting other drivers will also be discouraged on pure safety grounds.
The FIA is worried that even travelling at slow speed on the way to the pits, it is possible for something to go wrong and a driver sitting on the side of a car could fall off.