U.S. President Barack Obama made the proposal on Iran in a letter to his Russian counterpart, Dmitry Medvedev, Kommersant said, referring to unidentified U.S. officials.
Iran's controversial nuclear program was cited by the U.S. as one of the reasons behind its plans to deploy a missile base in Poland and radar in the Czech Republic. The missile shield has been strongly opposed by Russia, which views it as a threat to its national security. The dispute has strained relations between the former Cold War rivals, already tense over a host of other differences.
The leaders have exchanged letters and had a telephone conversation since Obama was sworn into office in January, Kommersant said. The first high-level Russia-U.S. meeting will take place later this week, when Russian Foreign Minister Sergei Lavrov meets with U.S. Secretary of State Hillary Clinton in Geneva.
Moscow has not yet responded to the proposal by Obama, the paper said, adding that a decision was unlikely to be made during Lavrov and Clinton's meeting.
The issue is likely to be discussed when Obama and Medvedev meet in London on April 2 on the sidelines of the G20 summit of world leaders to address the financial crisis. Earlier reports said Medvedev had also invited the U.S. leader to visit Russia and the date of Obama's first visit to the largest country in the world could be announced in the British capital.
In an interview on Sunday with Spanish media, Medvedev said he hoped to discuss the issue of missile defense with Obama in London. He also said he hoped the new U.S. administration would display a "more creative approach" to the issue than its predecessors.
"We have received signals from our American colleagues," Medvedev said. "I expect those signals will turn into specific proposals. I hope to discuss the issue, which is extremely important for Europe, with U.S. President Barack Obama."
The United States and other Western nations suspect Tehran of secretly seeking nuclear weapons. Iran says its nuclear program is purely aimed at generating electricity. However, unlike his predecessor, George W. Bush, Obama has stated a preference for diplomatic efforts to resolve the dispute.
U.S. Defense Secretary Robert Gates said on the NBC television channel on Sunday that the Islamic Republic was not close to building a nuclear bomb. "They're not close to a stockpile, they're not close to a weapon at this point, and so there is some time," Gates said.
Gates also said that while more sanctions should be imposed against Iran, the door should not be closed to diplomacy.