The coastal city Sochi is scheduled to host not only the Olympics but also a grand prix in 2014, with a 5.5km circuit to be situated in and around the Olympic village.
There have, however, been suggestions the race could be delayed to 2015, as the priority is the Olympics.
The respected Olympics website Around The Rings now reports that organisers could use the actual Olympic stadium, which is currently under construction, as part of the formula one circuit.
Known as Fisht Olympic Stadium and uniquely shaped like a shell, the 40,000-capacity and $63 million facility is within walking distance of the Olympic village.
The stadium is also touted to stage matches during Russia's hosting of the FIFA World Cup in 2018.
Around The Rings said the stadium is being designed so that structures in place for the Olympics can be removed to allow for the incorporation of the F1 circuit.
"This is something that has emerged as a possibility," a source in Sochi is quoted as saying. "It is an exciting possibility for formula one."