Already this week, the 28-year-old's manager Oksana Kosachenko revealed that "all the necessary work on our part is done -- and it's for Caterham to decide".
Petrov's teammate in 2012 was Finn Heikki Kovalainen, but Caterham has already announced that Charles Pic will be driving one of the green-liveried cars next year.
Among the other candidates to be Pic's 2013 teammate are Giedo van der Garde, Bruno Senna and Luiz Razia.
Turun Sanomat quotes Kosachenko as saying: "I believe Vitaly's race in Brazil securing tenth place in the manufacturers' championship helps us to stay where we were."
Also playing in Petrov's favour is a recent visit to Caterham's headquarters of his sponsor Russian Helicopters, and Bernie Ecclestone's desire to have a local driver on the grid when Russia hosts its inaugural grand prix in 2014.
Organisers of the 2014 race in Sochi said this week that construction of the track is now in "high gear".