A U.S. government official, who spoke on the grounds of anonymity, said the Trump administration is "in the midst of an internal process" of considering exceptions called SRE waivers, or significant reduction exemptions.
U.S. sanctions on Iranian oil purchases are due to take effect on November 4.
The Joint Comprehensive Plan of Action, a deal reached in 2015 by the Obama administration, meant sanctions on Iran were dropped in exchange for Iran limiting its nuclear activities.
White House National Security Advisor John Bolton said only last week that the administration wanted to avoid all waivers and see Iranian oil and gas exports entirely staunched, but that it might not be able to achieve that aim.
President Trump made a decision to leave the deal and reimpose sanctions.
Reuters had reported on Friday that India would buy 9 million barrels of Iranian oil next month.
Washington is pushing allies to cut imports of Iranian oil to zero and will impose a new round of sanctions on Iranian oil sales in November.
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The US has said that it will not make such concessions unless the North takes substantive steps to do away with nuclear weapons. Pompeo told South Korean President Moon Jae-in that the meeting was "another step forward " in the denuclearisation process.
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OnePlus 6T commercial availability to start end of October?
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Oil dropped below $83 a barrel on Monday, pressured by expectations that some Iranian oil exports will keep flowing after the US reimposes sanctions, easing a strain on supplies.
Brent crude oil prices fell more than 1 percent on Monday after Washington said it may grant waivers to sanctions against Iran's oil exports next month, and as Saudi Arabia was said to be replacing any potential shortfall from Iran.
LONDON-Oil prices started the week under pressure, amid reports the USA could grant waivers to some buyers of Iranian crude when oil sanctions on the Islamic Republic go into effect next month.
Last week, India reduced gasoline and diesel prices to give relief to consumers against rising global crude prices caused by uncertainty over USA sanctions on Iran and OPEC's decision to raise output. New Delhi and Tehran have reportedly discussed reverting to rupee trade after November 4.
"Chatter that Saudi Arabia has replaced all of Iran's lost oil" is weighing on prices, said Stephen Innes, head of trading for Asia-Pacific at futures brokerage Oanda in Singapore.
In May, US President Donald Trump announced America's withdrawal from the Iran nuclear deal. "Iran's oil can not be replaced by Saudi Arabia". He said that nine million barrels of oil are expected to be purchased.