Riyadh's production has spiked since June due to summer demand, reaching a record high in July of 10.67 million bpd and edging down to 10.63 million bpd in August.
From January to May, Saudi Arabia produced around 10.2 million bpd.
Two sources said Saudi Arabia's Gulf OPEC allies the United Arab Emirates, Qatar and Kuwait were expected to contribute to any reduction if an agreement were reached.
Saudi Arabia, by far the largest producer in the Organization of the Petroleum Exporting Countries, will shoulder the biggest cut, the sources said.
The proposal can be seen as a shift by Riyadh, which orchestrated the current OPEC policy in 2014 by refusing to cut output alone to support prices and chose to defend market share against rivals, particularly high-cost producers.
A fall in oil prices to $30-$50 per barrel from levels as high as $115 seen in June 2014 led to a boost in global oil demand and a decline in high-cost supplies such as those from the United States.
But the Saudi strategy caused a rift in OPEC, whose poorer members have faced a budget crisis and unrest. Riyadh and its Gulf allies also had to tighten their belts after a decade of generous public spending.
As the pain of cheap oil grew and pressures on Saudi finances increased, Riyadh and Tehran signaled they were willing to show more flexibility to prop up prices.
However, the first attempt at a global production pact collapsed in April when Riyadh insisted Tehran participate. Iran has said it will not join any such agreement until it regains market share and boosts output to pre-sanctions levels of around 4 million bpd.
OPEC members will meet on the sidelines of the International Energy Forum, which groups producers and consumers, in Algeria from Sept. 26-28. Non-OPEC producer Russia is also attending the forum.
Russian Finance Minister Anton Siluanov discussed the rumored deal on Friday with CNBC. Click here to read more.