The US space agency said earlier this year that it was exploring a programme called the Deep Space Gateway, a multi-stage project to push further into the solar system.
The project envisages building a crew-tended spaceport in lunar orbit that would serve as a "gateway to deep space and the lunar surface," NASA has said.
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And on Wednesday the Russian space agency Roscosmos announced that a cooperation agreement had been signed at an astronautical congress in Adelaide.
"The partners intend to develop international technical standards which will be used later, in particular to create a space station in lunar orbit," the Russian agency said in a statement.
The Russians and Americans would cooperate to build the systems needed to organise scientific missions in lunar orbit and to the surface of the Moon, the agency added.
"Roscosmos and NASA have already agreed on standards for a docking unit of the future station. Taking into account the country's extensive experience in developing docking units, the station's future elements will be created using Russian designs."
Igor Komarov, Roscosmos's general director, said no fewer than five countries were building their own rockets and systems.
"To avoid future problems over technical cooperation, part of the standards should be unified, for a possibility for various countries to work on their craft and dock to the international lunar station," Komarov was quoted as saying in the statement.
Russia and the United States also discussed using Moscow's Proton-M and Angara rockets to help create the infrastructure of the lunar spaceport, the statement said, adding that the main works were slated to begin in the mid-2020s.
Space exploration, including joint work on the International Space Station (ISS), is one of the few areas where international cooperation between Russia and the US has not been wrecked by tensions over Ukraine and Syria.
The $100 billion ISS, which has been orbiting Earth at about 28,000 kilometres (17,000 miles) per hour since 1998, is the world's largest space project.