That would surpass the previous high of 10.72 million in November 2016, according to Bloomberg.
Reports that the US wants to cut Iran oil imports to zero also contributed to the oil price gains.
"The kingdom's energy minister Khalid Al Falih indicated that members of the new deal with spare capacity - predominantly Saudi Arabia, its Gulf allies and Russian Federation - will increase output to make up for those that can not produce enough", reported FT.
But it said: "We are increasing our estimate of oil likely to come off the market by November to about 700,000 bpd - another bullish factor for prices".
Apple Inc, which rose 1.2 percent, snapped a three-day losing streak. Domestic oil use surges during summer months as the kingdom burns crude to generate electricity for air conditioning.
"The U.S.is continuing its decision to completely isolate Iran", said Gene McGillian, vice president of market research at Tradition Energy.
The rise in crude oil prices is always a concern for PSU oil marketing companies as these firms cannot pass any increase immediately.
Iran, the third-largest OPEC producer, faces the re-imposition of US sanctions on its oil exports after US President Trump's administration's withdrawal from the nuclear deal.
Trump renews attack on OPEC ahead of group's production meeting
In April, Trump also blasted OPEC on Twitter, accusing the group of "artificially" raising oil prices . USA crude inventories fell by 4.1 million barrels, to 432.4 million barrels.
West Texas Intermediate crude, the benchmark for USA oil prices, jumped by more than 2 percent on the news, to more than $70 a barrel.
Oil prices are in steep ascend which extends into second consecutive week and supported by several factors. Moreover, U.S. lawmakers have resurrected the "No Oil Producing and Exporting Cartels Act", or NOPEC, which proposes making the group subject to the Sherman antitrust law that was used more than a century ago to break up the oil empire of John Rockefeller.
Stephen Innes of futures brokerage OANDA said the outage had contributed to a major draw in USA crude oil inventories. "No good and will not be accepted!"
In North America, an outage at Canada's Syncrude has locked in more than 300,000 bpd of production, and operator Suncor Energy (SU.TO) said it will probably last at least through July.
The Organization of the Petroleum Exporting Countries, together with non-OPEC oil-producing nations such as Russian Federation, have agreed to raise daily output by 1 million barrels compared with the current level, effective July 1.
Matt Smith, director of commodities research at ClipperData, agreed: "If we are going to see more Iranian barrels coming off the market, that is likely to be bullish for USA exports". The aim of the organisation is to stabilise oil markets and steady the supply of oil for the public.
Oilprice.com, a prominent industry site said Saudi will have the final say on how much oil is added to the market.