The White House declined to comment on the report from the officials, who asked not to be identified, and the State Department said it could not confirm it.
If confirmed, the crashes would be a blow to the military strength Russia aimed to display in launching what it said were 26 missiles at Islamic State targets in Syria some 1,500 km (900 miles) from the Caspian Sea on Wednesday.
The Russian defence ministry denied any of the missiles had fallen short of their targets after reports of crashes first emerged on US television.
“In contrast to CNN, we do not talk with reference to anonymous sources,” the Russian Defence Ministry said. “We show the launch of our rockets and the targets they struck.”
Russia had displayed graphics of the missiles flying over Iran and Iraq on Wednesday.
US officials have already disputed Russian reports that the missiles stuck Islamic State fighters in Syria.