Iran's ambassador to the International Atomic Energy Agency, Ali Asghar Soltanieh, told the radio station he had struck a basic deal but details have still to be worked out.
But he did say that the joint enrichment company would operate on Russian soil.
Tehran claimed to have made an almost identical deal in February but the plan seemed to peter out when Iranian officials ruled out halting enrichment research on their own soil.
Iran says it has now successfully enriched uranium, a claim yet to be independently verified.
The compromise plan to move all sensitive nuclear work to Russia is designed to appease the United States and the European Union who have referred Iran to the United Nations Security Council and may demand sanctions.