President Obama reportedly made the offer during Israeli prime minister Benjamin Netanyahu's visit to Washington this week.
Under the proposed deal, Israel would not attack Iran until 2013, after US elections in November this year. The newspaper cited unnamed Western diplomatic and intelligence sources.
Netanyahu said Monday that sanctions against Iran had not worked, adding that "none of us can afford to wait much longer" in taking action against Iran's controversial nuclear program.
However, Netanyahu told FOX News Channel on Wednesday that he did not think war with Iran was inevitable. He added that the only way to deter Tehran was to advocate carrying out a serious military strike against the Islamic Republic.
"The paradox is that if they actually believe that they are going to face the military option, then you probably will not need the military option," Netanyahu said.
The US also believes there is still a "window of opportunity" for the dispute to be resolved diplomatically.
Obama told reporters during a White House news conference Tuesday that the US would apply pressure to Iran, "even as we provide a door for the Iranian regime to walk through" to prove its nuclear program is peaceful.
The President had met Netanyahu in the Oval Office the day before, where he reaffirmed his "unprecedented commitment" to Israel's security in the Middle East.
On Thursday, Iran's supreme leader Ayatollah Ali Khamenei welcomed Obama's support for finding a diplomatic solution to the Iranian crisis.
"This talk is good talk and shows an exit from illusion," AFP reported Khamenei as saying, citing the leader's website. However, Khamenei criticised the continued imposition of international sanctions against Iran.
"The US president continued saying that he wants to make the Iranian people kneel through sanctions, this part of this speech shows the continuation of illusion in this issue," he said.
A statement issued Thursday on behalf of the so-called P5+1 countries -- the US, UK, France, Russia, China and Germany -- urged Iran to enter into a "serious dialogue" and "without pre-conditions" on its nuclear program.
The statement was issued at a meeting of the UN atomic agency in Vienna. "We call on Iran to enter, without pre-conditions, into a sustained process of serious dialogue, which will produce concrete results," it said.
On Tuesday, the P5+1 countries accepted an offer from Iran's chief nuclear negotiator to resume talks.