The plane carrying 60 passengers and four crew collided midair with a military helicopter as it was approaching Reagan National Airport in Washington DC on Wednesday evening.
The state TASS and RIA news agencies, both citing a source, reported on Thursday that Shishkova and Naumov were on board the plane.
The agencies also reported that Inna Volyanskaya, a former pair skater who competed for the Soviet Union, was among the passengers.
Shishkova, 52, and Naumov, 55, competed at six world championships between 1991 to 1996, winning gold, silver and bronze medals.
The peak of their career was winning the 1994 pairs title at the world championships in Chiba, Japan.
After beginning their professional career in Russia, they moved to the United States, where they moved into coaching.
Local US media reported in 1998 that they had moved to the US state of Connecticut.
The Kremlin on Thursday confirmed that Russian citizens were on board the plane, saying it had seen “sad reports” the couple were among them.
Several members of the US figure skating community were also passengers, the sport’s national governing body confirmed.
They had been taking part in a training camp for top juniors that was held after the US championships, which took place in Wichita, Kansas, at the weekend.
“We are devastated by this unspeakable tragedy and hold the victims’ families closely in our hearts,” US Figure Skating said in a statement.
“Figure skating is more than a sport, it’s a close-knit family and we stand together,” the International Skating Union (ISU) added.
