Bridenstine, who became administrator in April, told the Post he has spoken "to many large corporations that are interested in getting involved" in the flying lab "through a consortium, if you will."
"We're in a position now where there are people out there that can do commercial management of the International Space Station," Bridenstine said in the interview, which was published Tuesday.
Bridenstine declined to specify which companies he had spoken to. Boeing was selected in August 1993 as NASA's primary contractor to develop and build the ISS. The aerospace giant's space division has continued to provide engineering and management under extended contracts. Boeing is tracking these developments as it works with NASA on future developments, according to the company's ISS spokesman, Steven Siceloff.
"Really what we're looking at is all of the entire commercial situation: The needs of both the station and the market," Siceloff told CNBC on Tuesday.
Siceloff said Boeing looks at future programs for the station "in the context of the ISS transition report," which NASA released in March. The report said nearly a third of NASA's $3.3 billion annual budget for the ISS is for operating costs. Siceloff said Boeing has reduced "operating costs 30 percent over the last 10 years."
Bridenstine has seven years to come up with a company or consortium to take on those costs because the White House announced plans in February to end NASA's funding of the ISS in 2025. Any transition would be inherently complex because the ISS is not a U.S. entity. It has agreements with nearly 30 nations to use the station, including Russia, the European Space Agency, Canada and Japan.
"It's healthy we're having this discussion today so we understand what the relationship is going to be between the government and the private sector," Jeff Manber, chief executive of space platform builder NanoRacks, told CNBC on Tuesday.
The ISS "is an integrated spacecraft," which means all its parts work together, Aerospace Industries Association vice president Frank Slazer told CNBC in February. Only a few elements "might be severable," Slazer added, saying that there "are details that have yet to be worked out."
The Trump administration in February also proposed a $150 million program to build commercial platforms in orbit, hoping to incentivize private companies develop alternative space stations.
To date, only a few companies are working to build private space stations. Two, Bigelow Aerospace and NanoRacks, have hardware on the ISS, while a third, Axiom Space, is set to launch its first module in 2020. Each of these companies is building a habitable craft to continue humanity's presence in low Earth orbit.
"We are focused on providing commercial platforms that augment the ISS," Manber said Tuesday. He said that NanoRacks envisions a future that will need the human and cargo transportation capabilities of SpaceX, Sierra Nevada Corporation and Boeing "for launches to service dedicated platforms" and habitats in space. The three companies have won funding from NASA to develop systems capable of sending astronauts to the ISS, with SpaceX and Boeing scheduled to begin flight tests this year.
When CNBC spoke to Bigelow Aerospace, NanoRacks and Axiom Space in February, none expressed interest in taking over the ISS. Each saw the ISS as a stepping stone to establishing commercial operations in low Earth orbit rather than the foundation on which to build.
"A wholesale taking over of the ISS is a very expensive endeavor," Axiom Space CEO Michael Suffredini told CNBC at the time.
Read the full report in The Washington Post here.