"A compromise is still possible," the source said.
"However, the current U.S. proposals are insufficient ... because the Bush administration is seeking to make the decision [on the deployment of the missile shield] irreversible and ... leave the new U.S. president without an alternative, putting on him the burden of responsibility for something that was decided without him," the source added.
Washington said last Thursday it had provided new proposals to ease Russia's concerns over the planned deployment of 10 U.S. missiles in Poland and a radar in the Czech Republic, which the United States said were needed to counter possible attacks from "rogue" states like Iran.
Russia, which says the missile defense system is a threat to its national security, has indicated it will not address the U.S. proposals until after President-elect Barack Obama is inaugurated in January.
Meanwhile, as an "asymmetric" response to the proposed U.S. missile shield in Europe, Russia announced the possible deployment of Iskander-M short-range missile systems in the Kaliningrad exclave, sandwiched between Poland and Lithuania on the Baltic Sea.
The Kremlin source said new discussions on the European missile shield should involve Russia, the United States and the European Union and must be based on respect for common interests rather than on a unilateral decision made by Washington.