Sources told Reuters that a ministerial panel of key OPEC producers and allies led by Russia recommended increasing production cuts by 500,000 barrels per day (bpd) from their current level of 1.2 million bpd.
The Organization of the Petroleum Exporting Countries will meet later on Thursday in Vienna followed by a meeting on Friday with Russia and other producers, a group known as OPEC+.
Brent crude futures were up 48 cents, or 0.78%, to $63.48 a barrel by 1350 GMT. Brent surged 3.6% on Wednesday. West Texas Intermediate (WTI) crude futures were up 23 cents to $58.66 a barrel, their highest since late September.
The OPEC+ group has been curbing output since 2017 to counter surging production from the United States, now the world's biggest oil producer thanks to rapid growth in shale oil output.
Next year, rising production in other non-OPEC countries such as Brazil and Norway threatens to add to the glut.
"We expect a constructive outcome to today's meeting in terms of a prolongation of the deal, but are not yet convinced that a strong bullish surprise with a sizeable adjustment to the target level will really transpire," Vienna-based consultancy JBC Energy said in a note.
OPEC's effort to deepen cuts and increase member compliance was also driven by the group's de facto leader Saudi Arabia's hopes to see higher oil prices to support its budget and initial public offering (IPO) of state-owned Saudi Aramco.
Oil prices surged on Wednesday on expectations of deeper OPEC cuts and data showing a large drop in U.S. crude inventories last week. But prices are still roughly where they were a week ago as concerns about a U.S.-Chinese trade war persist.
US President Donald Trump on Wednesday described trade talks with China as going "very well", a day after saying it could take until after next year's presidential election to complete an agreement.