"It now seems probable that the meeting will take place later in the week," said the source, who asked not to be named.
Oil prices have tumbled to levels not seen for decades due to the coronavirus outbreak, with an additional hit coming after Russia and OPEC kingpin Saudi Arabia failed to agree new production cuts and instead launched a price war.
Despite the happy talk in the oil sector, global stock markets fell following another set of devastating American employment numbers, gloomy eurozone services data and news that the number of declared COVID-19 infections passed one million worldwide.
The US economy shed 701,000 jobs in March amid the damage inflicted by the coronavirus shutdowns -- several times the market's consensus forecast -- while the unemployment rate surged to 4.4 per cent, the Labour Department reported.
That sent Wall Street to a sputtering finish, with the Dow losing 1.7 per cent and the S&P 500 and Nasdaq posting similar falls.
"The markets are digesting a larger-than-expected drop in March employment, which is likely to worsen on the heels of the past two weeks of spikes in jobless claims that approached the 10 million mark," analysts at the Charles Schwab brokerage said.
OPEC's move meanwhile sparked fresh speculation of an oil production cut, one day after US President Donald Trump ignited a record crude price rally by hinting that Riyadh and Moscow planned to end their price war with a sharp reduction in output.
According to a Russian source cited by the TASS agency, US officials also have been invited to take part in the meeting.
"It is in all parties' interests to agree to a significant cut," said Michael Hewson, an analyst at CMC Markets.
But even reducing output by 10 million barrels per day "is unlikely to be enough to push prices up much higher from here with demand on the floor," Hewson cautioned.
