The official did not say whether any specific intelligence led to the warning, which was not issued to the public.
ABC News first reported the warning.
Russian forces are on high alert to head off possible militant attacks at the Winter Olympic Games, which begin on Friday in Sochi. Some US lawmakers have expressed concern about security at the Black Sea resort, but US President Barack Obama has said he believes Sochi is safe.
Suicide bombers killed 34 people in the Russian city of Volgograd, 400 miles (700 km) northeast of Sochi, in December. The attacks raised fears of violence at the Olympics.
US security officials said they were not aware of any specific threats to the United States now.In 2009 a Nigerian man tried to set off an explosive hidden in his underwear aboard a US-bound airliner. In 2001 a man tried to blow up a jumbo jet with explosives in his shoes.