Such an increase would bring compliance with agreed supply curbs down to 100 percent from April's level of around 152 percent, the sources said.
The initial talks are being led by the energy ministers of OPEC kingpin Saudi Arabia and Russia at St. Petersburg this week along with their counterpart from the United Arab Emirates, which holds the OPEC presidency this year, the sources said.
OPEC and non-OPEC ministers meet next in Vienna on June 22-23, and the final decision will be taken there.
The Organization of the Petroleum Exporting Countries and non-OPEC producers led by Russia have agreed to curb output by about 1.8 million bpd until the end of 2018 to reduce global stocks, but the inventory overhang is now near OPEC's target.
The current discussions are aimed at relaxing record-high compliance with the production cuts, the sources said, in an effort to cool the market after oil hit $80 a barrel on concerns over a supply shortage.
While Russia and OPEC benefit from higher oil prices, up almost 20 percent since the end of last year, their voluntary output cuts have opened the door to other producers, such as the U.S. shale sector, to ramp up production and gain market share.
The final production number is not set yet as dividing up the extra barrels among deal participants could be tricky, the sources said.
"The talks now are to bring compliance down to the 100 percent level, more for OPEC rather than for non-OPEC," one source said.
OPEC may decide to raise oil output as soon as June due to worries over Iranian and Venezuelan supply and after Washington raised concerns the oil rally was going too far, OPEC and oil industry sources told Reuters on Tuesday.
However, it is unclear which countries have the capacity to raise output and fill any supply gap other than Gulf oil producers, led by Saudi Arabia, and Russia, the sources said.
"Only a few members have the capability to increase production, so implementation will be complicated," one OPEC source said.
OPEC’s compliance with the output deal reached unprecedented levels in recent months, meaning it had cut well above target. Falling Venezuelan output due to an economic crisis has helped OPEC deliver a bigger cut than intended.
So far, OPEC had said it saw no need to ease output restrictions despite concerns among consuming nations that the price rally could undermine demand.
The rapid decline in oil inventories and worries about supplies after the U.S. decision to withdraw from the international nuclear deal with Iran, as well as Venezuela’s collapsing output, were behind the change in OPEC's thinking.
Concerns raised by the United States that oil prices were too high also made the exporting group start internal discussions, OPEC sources familiar with the matter have said.
U.S. President Donald Trump, whose country is a major oil producer but is not part of the supply-cutting pact, last month said OPEC had "artificially" boosted oil prices. - Reuters