Bianchi remains in intensive care after suffering a severe head injury when he collided with a recovery vehicle during last weekend's race in Japan.
While Marussia have yet to formally announce Rossi's drive, they have registered the American rookie as one of their two eligible drivers for this weekend's Sochi race, alongside Max Chilton.
Rossi, 23, has already driven for the team twice during Grand Prix weekends, competing in FP1 at Montreal, Canada, and Spa-Francorchamps, Belgium.
Alongside Rossi, there will be two driver changes for FP1 at the Sochi Autodrom. Russia's Sergey Sirotkin will drive for Sauber, thereby making his Grand Prix weekend debut on home soil, while Roberto Merhi will once again drive for Caterham, the third time he has contested a practice session for the team this season.