It was not clear how much Saudi Arabia offered to cut on its own.
OPEC+ sources told Reuters that Russia and Kazakhstan were pushing for the group to raise production by 500,000 barrels per day (bpd) while Iraq, Nigeria and the United Arab Emirates suggested holding output steady.
An internal OPEC+ document, seen by Reuters on Tuesday and dated Jan. 4, set out several scenarios for 2021, including the possibility of cutting by 500,000 bpd in February.
It highlighted bearish risks and “stressed that the reimplementation of COVID-19 containment measures across continents, including full lockdowns, are dampening the oil demand rebound in 2021”.
Three OPEC+ sources said chances of a collective cut were slim as very few producers supported it and most countries favoured either steady supply or an increase in February.
Saudi Energy Minister Prince Abdulaziz bin Salman on Monday said OPEC+ should be cautious, despite a generally optimistic market environment, as demand for fuel remained fragile and variants of the coronavirus were unpredictable.
New variants of the coronavirus first reported in Britain and South Africa have since been found in countries across the world.
OPEC+ producers have been curbing output to support prices and reduce oversupply since January 2017.
As COVID-19 hammered demand for gasoline and aviation fuel, benchmark Brent oil futures plunged below $16 a barrel last April, forcing OPEC+ to boost its output cuts to a record 9.7 million bpd in mid-2020.
With Brent holding above $50 per barrel, OPEC+ took the opportunity to raise output by 500,000 bpd in January, putting its current cuts at 7.2 million bpd.
Brent was trading up nearly 4% at above $53 per barrel at 1626 GMT.