Russian and NATO officials are meeting Monday in Moscow to discuss a plan that will give Russia a greater say in the alliance's affairs.
Russian and NATO officials would like to have an agreement ready to bring to a meeting in Reykjavik, Iceland, next week.
According to the Russia's Itar-Tass news agency, Russian officials on Monday reported there is a "strong chance" that the two sides would be able to come up with an agreement before the Reykjavik meeting.
The Iceland meeting will include foreign ministers from Russia and NATO member-countries who will review the agreement governing relations between Moscow and the alliance.
If the proposed agreement meets with approval, there will be a formal signing ceremony at the end of May during the NATO-Russia summit in Rome.
The agreement would create a new "Council of 20" that will give Russia a greater voice in NATO affairs. The Council of 20 will replace the Permanent Joint Council, which was called the "19 plus one."
Russia often criticized the Permanent Joint Council, saying it simply presented Russia with decisions the 19 NATO member countries had already agreed upon.
Under the new arrangement, Russia and NATO members would meet as equals on a limited range of subjects including anti-terrorism, arms proliferation, management of regional crises and peacekeeping, and search and rescue efforts.