About 6,000 members of delegations, including 3,000 athletes, are expected to take part in the Sochi Games, Chernyshenko said on Friday, media reported. (Agencies)
"By now, about 40 heads of states and governments are planning to visit Sochi," Chernyshenko told a meeting of the Parliament's Lower House, or State Duma.
He assured the Parliament that there has been enough snow in Sochi to hold competitions smoothly.
Over 52cm of snow fell in the Russia's only subtropical city overnight, according to the federal meteorological centre.
Nearly everything in the Black Sea resort has been ready for the Games, Russian Olympics Committee president Alexander Zhukov said during the same meeting.
"According to everyone's opinion, all venues built in Sochi are not just new, they are unique. Many of them are the world's best," he said.
Also on Friday, the Olympic torch has been relayed to the Russian Olympic champion Svetlana Zhurova after its return from the International Space Station.
At the ceremony held in the Star City cosmonauts training centre near Moscow, a representative of the Russian Space Agency Roscosmos handed the torch over to Zhurova.
The torch spent nearly six hours in the open space during a spacewalk by two Russian cosmonauts, on November 9.
The 22nd Winter Olympic Games will take place on February 7-23, 2014.
About 6,000 members of delegations, including 3,000 athletes, are expected to take part in the Sochi Games, Chernyshenko said on Friday, media reported.