It is understood that Sebastian Vettel has written personal letters of apology to both the FIA president Jean Todt and Charlie Whiting.

The move comes as the FIA investigates the German's outburst in the final laps of Sunday's Mexican Grand Prix.

As the German awaited news on Max Verstappen who had run wide and was supposed to hand track position back to the Ferrari driver, who was under increasing pressure from Daniel Ricciardo as the Dutch youngster deliberately backed Vettel into his clutches, his engineer came on the radio.

"Charlie said that…"

Vettel cut in: "Yeah! You know what? Here is the message for Charlie: '**** off! Honestly, **** off!"

While Vettel apologised to Whiting in person immediately after the race, the FIA has since launched an investigation into the outburst which could cost the German a fine or even a race ban.

Assuring both Todt and Whiting of his regret at his outburst, Vettel will be hoping the FIA takes a lenient view of the matter.

Though Whiting is understood to have accepted Vettel's apology at the time - a long-time friend of Bernie Ecclestone he will have heard much worse over the years - reaction to the outburst, particularly from the like of Red Bull has forced the FIA into a corner.

Whatever one's view of the outburst, and one has to realise that F1 is one of the only sport's where a player in the heat of competition is subject to having every word uttered broadcast to the world, one has to wonder why the person charged with broadcasting the event allowed the rant to be made public.

Then again, when one looks at the publicity the outburst has attracted, especially after what was, for the most part, a pretty processional race, perhaps one can see the method in the madness.