The proposal, which is backed by Washington and the European Union, involves the creation of a joint Iranian-Russian company to enrich uranium in Russia.
The plan has been put forward by Moscow in a bid to allay international concerns that Iran could manufacture highly- enriched uranium on its own soil to build atomic weapons.
Iran says it only wants to enrich uranium to a low-grade, suitable for use in atomic power reactors.
Iranian officials had previously said they would reject any plan which denied Iran the right to build its own uranium enrichment facilities.
But, in a sudden change of tone, a senior official had said on Wednesday Tehran would "seriously and enthusiastically" study the Russian plan.
The diplomat, speaking to Reuters on condition of anonymity, said the agreement for talks on the proposal came during a telephone conversation between Iran's chief nuclear negotiator Ali Larijani and Russian Security Council Secretary Igor Ivanov.
Larijani told Ivanov there were "ambiguities and problems" with the Russian plan but that "the outline of the proposal can be reviewed," the diplomat said.
Ivanov agreed to send a delegation to Tehran led by one of his deputies for further talks, the diplomat said, without specifying when they would take place.
Ivanov, who has a record of holding unofficial talks on tricky foreign policy issues for the Kremlin, was not immediately available for comment.
The Russian foreign ministry said it had not received any official reaction from Tehran to its proposal aimed at defusing the situation.
"We have not received any reply from Iran after sending them our proposals and our position remains unchanged," a foreign ministry spokesman told Reuters.
EU diplomats and arms control experts have noted that Tehran has been careful to stop short of flatly rejecting Moscow's plan, which could weaken Russian opposition to EU and US efforts to refer Iran to the UN Security Council for possible sanctions. They say Iran may be willing to drag out talks about the Russian proposal to buy time and good favour.
The Iranian diplomat said that both Larijani and Ivanov had noted that their talks on the Russian proposal were unrelated to Iran's ongoing nuclear negotiations with the EU trio of Britain, Germany and France.