Russian space officials say they will select the winning design this month for the rocket intended to carry cosmonauts to the moon within a decade.
Alexander Chulkov, head of the rocket and launch facilities directorate at Russia's space agency, Roscosmos, told the BBC News the winner will be picked by March 25.
"We have a bidding procedure, under which we made a request for proposals and now will be reviewing those proposals to determine a prime developer, based on the most interesting project from the cost-effectiveness point of view," Chulkov said.
The primary requirement is for the rocket to carry 20-23 tons into low-Earth orbit, the British network reported Monday. That's about three times as heavy as the Soyuz capsule cosmonauts have ridden into space since 1967. It's also to use environmentally friendly fuels, the BBC said.
The first test launch of the new rocket is expected about 2015 with the first manned launch in 2018.
The United States, the only country to put a man on the moon, has announced plans for its Constellation program to return astronauts there by 2020.
China, India, Japan and Europe also have announced lunar exploration programs.
All major Russian space firms reportedly entered the competition for the rocket contract.
"Roscosmos has its own opinion about the configuration (of the rocket), which we would like to see, however, we understand there is some distance between what we want and what might be available," Chulkov said.