Frenchman Todt, 75, is stepping down as FIA president in just over a week, with Graham Stoker and Mohammed ben Sulayem vying to be elected as his successor.
Prior to becoming FIA president, Todt was the ultra-successful team boss at Ferrari, where he oversaw the entire Michael Schumacher era and beyond.
Corriere della Sera newspaper in Italy now reports that he may be coming back to Maranello in an advisory role, with talks between Todt and Ferrari chairman John Elkann said to have already taken place.
According to sources, Todt's role would leave the team principal role to Mattia Binotto, freeing up the Italian to focus on performance rather than politics.
Giogio Terruzzi, writing for Corriere della Sera, said it might be referred to as a "super consultant" role for 2022 and beyond, helping Binotto with political but also "sporting issues".
RMC Sport quotes Todt as saying that he is "a little bit sad" about stepping down as FIA president next Friday.
"I often talk about it with relatives and say that I'm 70 percent happy and probably a little bit sad, 30 percent, so you can see that I am a lot more positive than negative about leaving after 12 years," he said.