The official list of cars and drivers published by stewards on Thursday named Rossi and Britain's Max Chilton as Marussia's entrants.
There was no official statement from Marussia but sources made clear a decision had yet to be taken about how to proceed out of respect for Bianchi's family and a desire to 'do the right thing' for their stricken team mate.
Bianchi suffered a brain injury and remains 'critical but stable' in a Japanese hospital after his horrific crash at Suzuka last Sunday.
There have been no medical updates since Tuesday.
The popular Frenchman's car aquaplaned off a wet circuit, in fading light, and into a tractor that was recovering a crashed Sauber.
Marussia, a small and financially struggling team who have punched above their weight this year thanks to Bianchi, are expected to wait until Friday morning to confirm how they plan to proceed.
Putting down Rossi's name fulfills the regulations but there is a strong chance Chilton will be their only race entrant in what should have been a big moment for the sport's only Russian-registered team on Russia's F1 debut.
Although the rules stipulate that a constructor must 'participate' in every event as a team, the act of entering two cars for official scrutineering has satisfied that already.
Marussia can also count on the full support of the powers that be for whatever they decide to do.
The team, whose current standing of ninth in the championship is due to Bianchi's points finish in Monaco in May, have been overwhelmed by a groundswell of support from the rest of the paddock and wider world.
Formula One supremo Bernie Ecclestone has kept in regular touch, offering whatever support may be needed, while FIA president Jean Todt is in close contact through his son Nicolas, Bianchi's manager.
Ferrari, for whom Bianchi was a test driver being groomed for a stellar future, arranged for a leading Italian neurosurgeon to fly to Japan along with the French professor who attended to seven times world champion Michael Schumacher after the German's skiing accident last year.
Bianchi's name was alongside Chilton's above the team's garage on Thursday, and is set to stay there, with mechanics going through the normal procedures of setting up both cars in the bays.
However the team's British principal John Booth has stayed behind in Japan to be with Bianchi's family at the Yokkaichi hospital and is not travelling to Sochi.
The shock of the crash hung heavy over the paddock, with drivers still stunned by what had happened and expressing support for their colleague.
All will race on Sunday with stickers saying 'Tous avec Jules #17' (All with Jules), a reference to the 25-year-old's driver number, on their helmets.
"Obviously all of our thoughts are with Jules. All of our minds are there," said Ferrari's Fernando Alonso.
"Emotionally very difficult. Ready to race, to race for him, being as professional as we can but definitely our minds, or my mind, is with him in this moment, praying for him."
(Reporting by Alan Baldwin, editing by Justin Palmer)
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