The government's endorsement would make way for Moon Express, a relatively obscure space startup co-founded by Naveen Jain, to land a roughly nine-kg package of scientific hardware on the Moon sometime next year, said the report.
The company appears close to obtaining what it has called "mission approval", the Wall Street Journal reported late Sunday, citing unnamed sources familiar with the details.
It could be first in an array of for-profit ventures throughout the solar system.
The decision is expected to set important legal and diplomatic precedents for how Washington will ensure such nongovernmental projects comply with longstanding international space treaties.
The formal approval, which could be months away, may also pave the way for potential commercial space tourism and asteroid mining ventures.
"We've been a regulatory pathfinder out of necessity," because up to now "only governments have undertaken space missions beyond Earth orbit," Moon Express CEO and co-founder Bob Richards told the Journal.
The proposed mission still poses huge technical obstacles for Moon Express, including the fact that the rocket it wants to use has not yet flown, the Journal said.
Moon Express was founded in August 2010. The company is developing innovative, flexible and scalable new robotic spacecraft that will radically reduce the cost of space exploration and unlock the mysteries and resources of the Moon, according to its official website.