"The number of details that need to be agreed is such that it's physically impossible to do it all in the time left until the end of the year," the Russian source told Interfax.
"Such delays shouldn't be dramatized, since Moscow and Washington are both equally keen on constructive (dialogue) and on coming up with a document that suits both sides," the source told Interfax.
The source said the documents "may be ready for signing in January next year."
The report comes a day after a US official, speaking to reporters on condition of anonymity, said the US does not expect to sign a successor agreement to the Strategic Arms Reduction Treaty, or START, this year.
A State Department official suggested a deal would not even be signed in the next two weeks.
US officials, he said, "expect that the START talks are powering right through the weekend, they're going to go right up to Christmas (then) breaking for the holidays and coming back in January.