Russia's Energy Minister Alexander Novak, Saudi Arabia's Energy Minister and OPEC conference president Khalid al-Falih, and OPEC Secretary General Mohammad Barkindo attend a meeting of the Organization of the Petroleum Exporting Countries (OPEC) and non-OPEC producing countries in Vienna, Austria, May 25, 2017.

Saudi Arabia and a group of OPEC members are reportedly trying to commit Russia and other oil-producing nations to continue managing supply for up to three more years.

The so-called OPEC+ coalition reached a historic deal in 2016 to slash output in a bid to end a punishing oil price downturn. The group of two dozen producers briefly lifted the caps last year, but agreed to fresh production cuts in December after a three-month collapse in oil prices.

OPEC Secretary General Mohammed Barkindo and some oil ministers have long sought to make the alliance permanent, but Russia essentially nixed that idea in December.

Now, some OPEC nations including Saudi Arabia and the United Arab Emirates are trying to lock their allies into another several years of coordination, the Wall Street Journal reports. Some of the nations are expected to debate the proposal when they meet in Vienna later this month, according to the Journal.

"It is an effort to put a formal framework around an ad hoc relationship," Helima Croft, global head of commodities strategy at RBC Capital Markets, told CNBC. She said OPEC clearly does not want Russia to abandon them.

An OPEC spokesperson was not immediately available to comment.

One OPEC official told the Journal the prospect of another price crash is pushing coalition members to agree on some sort of arrangement. A vow to continue cooperation would support oil markets because it would reassure traders the OPEC+ backstop would remain in place.

Brent crude has rebounded about $12 a barrel to about $62 a barrel after tumbling 42 percent, but the international benchmark is struggling to break through resistance around $65 a barrel.

Moscow is better positioned to balance its budget at current levels than Saudi Arabia, which needs Brent prices at about $73 a barrel to break even, according to the International Monetary Fund.

However, the new proposal is likely to face opposition from within the coalition. Iran in particular opposes steps towards institutionalizing the alliance, OPEC sources tell the Journal. The Islamic Republic worries that would concentrate decision-making in the hands of Moscow and Riyadh, its chief regional rival.

Russia and Saudi Arabia are the second and third biggest oil producers, respectively.

In recent years, a smaller group within the coalition tasked with monitoring compliance to production quotas — the Joint Ministerial Monitoring Committee — has increasingly dominated the conversation. The Journal reports that Iran and non-OPEC member Oman have sought to reduce the number of JMMC meetings.

Other OPEC members including Algeria, Angola, Iraq and Nigeria have also pushed back on the idea of a permanent coalition that gives the Saudis and Russians more influence, according to the Journal.

In December, Russian Energy Minister Alexander Novak poured cold water on the idea.

"There is a consensus that there will be no such organization. That's because it requires additional bureaucratic brouhaha," Novak said, noting bipartisan U.S. legislation aimed at breaking up OPEC.

NOPEC, or the No Oil Producing and Exporting Cartels Act, would authorize the Justice Department to sue groups like OPEC that are deemed cartels for price fixing and antitrust violations, stripping countries of sovereign immunity protections currently built into U.S. law.