The plan would initially see two private trips a year, lasting 30 days each. The cost would be substantial: US$50m ($16m) for the flight and $35,000 ($53,00) "hotel" charges a night per person.
Jeff DeWit, Nasa's chief financial officer, made little secret of why he wanted to bring in private cash when he told CNBC that it would help "lower the cost and lower the risk" of exploration.
Private involvement in Nasa is hardly new. A raft of private companies, including Elon Musk's SpaceX, have been ferrying cargo to the space station for some time.
Over the next few months, trials should be completed to allow SpaceX and Boeing to begin carrying astronauts to the station, meaning that the US will no longer depend on the Russians to provide the shuttle service.
While big players such as Musk, Jeff Bezos and Sir Richard Branson have garnered headlines, a host of smaller companies are also using the space station as commercialisation gathers pace.
There are companies, such as Made In Space, already operating at the station. It produced space's first ever manufacturing device – a 3D printer.
Nasa's revived interest in the moon has also opened up business opportunities. For example, nine companies are competing for lunar transportation contracts worth $2.6b ($3.9b).
"The various space-related technologies out there are improving drastically, creating new investment opportunities," says Andrew Chanin, chief executive of ProcureAM, an investment company specialising in the sector.
"In the first space race, almost the entire endeavour was paid for by governments. Now they account for only 20pc of investment.
"The barriers to entry have come down. Reusable rockets have reduced the time between missions as well as reducing the cost. Satellites are getting smaller, lighter and far more powerful.
"Government space agencies are less inclined to say they don't want to get involved with third parties."
The plethora of small companies has created the opportunity for ProcureAM's fund, which has the stock exchange ticker "UFO".
Tess Hatch, an investor at Bessemer Venture Partners in Silicon Valley, is also enthusiastic about the opportunities the new space race affords.
"It's wonderful that these private companies are paving the way to making humanity multi-planetary by exploring Mars, but they also will need to work with the government and Nasa to get there," she says.
"The International Space Station will be decommissioned eventually and we don't want to lose having access to a space station in low earth-orbit as we did with the moon.
"Therefore, Nasa is encouraging private companies to develop technology for a replacement. However, private companies need a commercial purpose or reason and way to make money with this endeavour."
But Jonathan McDowell, an astrophysicist at the Harvard-Smithsonian Center for Astrophysics, believes Nasa chiefs are making a virtue out of necessity.
"They are hoping to offset the cost of running the International Space Station by privatisation," he says.
"Nasa is getting bored with the space station. It wants to send astronauts to the moon and Mars. It wants to spend its money on the space launch system rocket, the Orion spaceship, the lunar lander and lunar gateway.
"But these things are super expensive and it is not clear where the money to run these things and the super expensive space station is coming from."
McDowell doubts privatising the space station can work, given it will be retired by the end of the 2020s. The commercial opportunities for the private sector in space remain hazy, he adds: "It is not clear if the market is really there.
"It is one thing to fly experiments to the space station for a small charge and taking care of much of the cost. But when you start charging real money, I don't think there will be many takers."
About: SpaceX
Also known as: Space Exploration Technologies Corporation
What: A privately-funded aerospace company
CEO: Elon Musk
Founded: June 2002
Headquarters: California
Major achievements to date:
• Successfully launched the Falcon 1 rocket into orbit (2008)
• Launched, orbited and recovered the Dragon spacecraft (2010)
• Delivered supplies to the ISS on the unmanned Dragon cargo ship (2012)
• Launched its first commercial satellite, SES-8, into orbit (2013)
• Launched DSCOVR - a deep-space observatory that aims to alert people on Earth of potentially dangerous solar activity and geomagnetic storms (2015)
• Successfully launched and landed the Falcon 9 rocket - a major milestone in the drive to cut costs and waste by making rockets as reusable as planes (2015)
• Successfully launched the Falcon Heavy, currently the space vehicle with the highest payload available (2018)
