Riyadh's expected production increase – the second in two months – would lift flows above 9.5 million barrels per day (bpd) from about 9.45 million bpd now, the sources said.
The Saudi output plans come to light a week before the kingdom hosts an unprecedented meeting of producers and consumers to tackle market instability.
A relentless rise in oil prices to well above $130 (Dh478) a barrel has sparked fuel protests from Asia to Europe and roiled financial markets as policymakers fear higher inflation will slow the global economy.
"Saudi output in July most probably will be above 9.5 million," said one industry source, speaking on condition of anonymity.
"The situation right now is 'if the customers ask, they will get.'"
Saudi Arabia has already increased supply by 300,000 bpd this month from May to meet demand from buyers primarily in the United States.
Industry insiders declined to say how much more the kingdom would pump in July, but one source said output would not reach 10 million bpd.
Oil fell nearly $2 a barrel on Friday after industry newsletter the Middle East Economic Survey reported Riyadh was considering a sizeable output increase to near 10 million bpd.
The New York Times, citing analysts and oil traders briefed by Saudi officials, also reported the kingdom intends to increase oil output in July by some half-million barrels a day.
US crude has more than doubled in a year to strike a record $139.12 a barrel earlier this month.
The sky-rocketing price has led many countries – including top consumer the United States – to call on the Organization of the Petroleum Exporting Countries, and Saudi Arabia in particular, to boost output.
Supply plans by core Opec members could see exports from the Gulf rising by close to one million bpd this month and next.
US Treasury Secretary Henry Paulson warned on Saturday that oil's rally could prolong the US economic downturn.
The kingdom is also concerned about the effects of costly fuel and intends to address the issue at its urgently called meeting on June 22 in Jeddah.
"I don't know if the Jeddah meeting will reverse the trend of rising oil prices, but it will certainly show that Saudi Arabia and Opec are making every effort not to be the cause of the problem," said an oil industry expert.
Saudi Arabia is the only member of Opec with the spare capacity to boost supplies quickly and significantly. It could pump around 2 million bpd more than it does.
The last time the kingdom pumped more than 9.5 million bpd was in November 2005, according to Reuters' monthly surveys.