After a tumultuous couple of years, the 23-year-old Russian lost his place not only at Toro Rosso, but in the entire Red Bull programme.
But Formula E is now regarded as a viable alternative to F1 for drivers, manufacturers and sponsors.
Ex-F1 drivers including Jean-Eric Vergne, Sebastian Buemi, Kamui Kobayashi, Nelson Piquet jr, Andre Lotterer, Lucas di Grassi, Jerome d’Ambrosio and Nick Heidfeld all race in Formula E today.
Felipe Massa is expected to follow soon, and the Russian news agency Tass says Kvyat is another potential Formula E driver of the future.
Tass says Kvyat has “held talks with at least two teams” and could take part in test drives in January.