FIA believes there is no cause for Ferrari to lodge an appeal that, if successful, would strip Vettel of the F1 title and give it to Ferrari driver Fernando Alonso.
Video footage from Sunday's Brazilian GP appears to show that Vettel passed Jean-Eric Vergne's Toro Rosso's while a yellow caution light was on.
If a rules breach were proven, Vettel would be hit with a 20-second penalty, which would move him from sixth place to eighth in the race and give Alonso the F1 title by one point.
"The incident wasn't reported to stewards in the first place because it didn't seem like there was a need to report it at the time," Norman Howell, the director of communications for the International Automobile Federation (FIA), told The Associated Press. "Now that Ferrari has sent us a letter asking for an explanation we will give it to them."
One of the videos was taken from a camera on Vettel's car.
"Ferrari has asked, via a letter, an explanation from the FIA over VET's pass of VER on lap 4 of the Brazilian GP," the Italian team said in a Twitter post Thursday.
Alonso finished second in the race at Interlagos, but Vettel's sixth place was enough to give him his third straight season title by three points. The 25-year-old German became F1's youngest three-time champion.
Should Alonso be awarded the title, he would become a three-time champion.
"We're looking at the video. We have until tomorrow to file an appeal," Ferrari spokesman Luca Colajanni told The AP.
If Ferrari does appeal, the case would then be considered by the four Brazilian GP stewards. After an eventual decision, each side can appeal to the FIA appeals court, with a final decision likely before the F1 awards ceremony in Istanbul on Dec. 7.
Vettel appeared to be in big trouble when he was bumped shortly after the start of the race and spun. He dropped to last place before he could turn his car around and began to chase the leaders. He steadily worked his way up the field despite a slightly damaged car and no radio communication.
It was during Vettel's climb back through the field that the alleged illegal overtake of Vergne occurred.
When there is a yellow caution flag or light, it signals danger on the track and drivers must slow down and not overtake. If a driver does overtake, he is penalized with a drive-thru or a 20-second penalty in the final results if the infraction is discovered after the race is over.