The Organization of the Petroleum Exporting Countries and allies including Russia are expected to extend output cuts this week and could increase the size of the curb by at least 400,000 barrels per day, two sources said.
Brent crude, the global benchmark, rose $1.20 to $61.69 a barrel by 0825 GMT. U.S. West Texas Intermediate (WTI) crude added $1.05 to $56.22.
The so-called OPEC+ group has coordinated output for three years to balance the market and support prices.
Their current deal to cut supply by 1.2 million bpd that started in January expires at the end of March 2020.
"Any sign of discontent between the producers will send out negative signals and will put significant downward pressure on the oil price," said Tamas Varga of oil broker PVM. "We believe this is unlikely to happen."
OPEC's ministers will meet in Vienna on Thursday and the wider OPEC+ group will gather on Friday.
On Friday, Brent and U.S. crude both fell on concerns that talks to end the trade war between the United States and China, the world's two biggest oil consumers, would be disrupted by U.S. support for protesters in Hong Kong.
Oil also rose on Monday due to an unexpected return to growth in Chinese factory activity in November as domestic demand picked up on Beijing's accelerated stimulus measures. That is supportive of the oil demand outlook.
But U.S. production keeps rising led by shale oil, filling the gaps left by OPEC, with output in September increasing to a new record of 12.46 million bpd, the U.S. government said in a monthly report on Friday.
It is not certain that OPEC+ will agree this week to deepen its curbs. Some in the group are wary of encouraging more U.S. production by measures to support prices.
"A deeper cut could boost prices, which would bring on more shale output and not help," the OPEC source said. "If WTI goes up to $60, there will be more shale."