The deal, which already includes Venezuela and Qatar, is scheduled to be finalised at a meeting in Doha on 17 April and is expected to see output constrained to January levels.
Other Opec members are expected to attend, though non-Opec Oman claims it is yet to receive an invitation despite indications from Saudi Arabia it would try to bring in all oil producing countries.
Russia, who's seen its rouble fall in line with the oil price over the past 20 months, has been pushing for a deal for the past few months.
In February Russian president Vladimir Putin promised no Russian oil company would raise production in 2016 and recent output numbers have supported that statement.
“There is agreement from many countries to go along with a freeze — why make it contingent on Iran,” an Opec delegate reportedly told the Financial Times.
The oil price initially fell during the trading session today following news of bombings at a Brussels airport and train station that has left at least 30 people dead, though has since climbed back into positive territory.
International benchmark Brent crude hit $41.73 per barrel in trading earlier today, up 50 per cent from lows of $27 in January. US oil, West Texas Intermediate, has seen a similar rebound and is now near parity with Brent at $41.30.
Saudia Arabia lead Opec has been working to bring non-Opec countries onboard with its production controls after its falling market share of the worlds oil supply meant that it was unable to prop up the price without help other.
US output of expensive shale oil has surged over the past 10 years, with production from Russia and other countries also growing.