Obama made the proposal in a secret letter that was hand-delivered to Medvedev three weeks ago, the newspaper reported, citing anonymous U.S. sources.
A senior U.S. official confirmed to Reuters that Obama had sent a letter on the subject to his Russian counterpart.
"We can confirm that President Obama sent a letter to President Medvedev," the senior U.S. official said. "The letter touched on a range of subjects, including missile defense and how it relates to the Iranian threat."
Russia has vigorously opposed the missile shield, which would include sites in the Czech Republic and Poland, since it was proposed by the Bush administration. The stated aim of the shield is to deter Iran from launching nuclear-tipped missiles at U.S. allies in Europe.
According to the report, Obama's letter said the United States would not need to build the missile defense system if Iran's efforts to build a nuclear weapon were halted.
Moscow has not yet responded to Obama's offer, the report said.
U.S. Secretary of State Hillary Clinton is set to meet with Foreign Minister Sergei Lavrov in Geneva on Friday.
William Burns, the State Department's political director and a former U.S. ambassador to Russia, went to Moscow in February to help prepare for that meeting and to broach ideas to improve ties.
Burns indicated compromises on missile defense, telling Russian officials the Obama administration was willing to slow plans for a shield in Eastern Europe if Russia agreed to help stop Iran from developing nuclear weapons.
U.S. Vice President Joe Biden has signaled the Obama administration's wish to change tack with Russia, telling a security conference in Germany that it was time to hit the "reset" button with Moscow.
Lavrov urged the United States on Monday to restore diplomatic relations with Iran, Russian news agencies reported. "This would be an important element in stabilizing the situation in the region," he said.
Iran is just one of the issues that will test the relationship between Russia and the U.S. under Obama, whose election has raised hopes of improvement after bitter under the Bush administration.
Arms control is expected to be a main topic of Lavrov's talks with Clinton as the nations prepare to seek a replacement for the 1991 START I nuclear arms treaty, which expires in December. Both indicate they are ready for further cuts.
But Lavrov pressed ahead Monday with the tough stance he laid out last month, saying Russia wants limits on all nuclear warheads, not just those deemed "operationally deployed," and wants to cut not just warheads but also the missiles, bombers and submarines that carry them. (AP, Reuters)
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