The Onion, the humor publication, weighed in on the subject 14 years ago: “Coke-Sponsored Rover Finds Evidence of Dasani on Mars.”

NASA’s own documents appear to prohibit such activities. A webpage from the agency’s general counsel office states: “The rule is simple: we may not use our public office for private gain. This includes our own private gain, or that of anyone else.”

It adds, “Federal employees may not endorse through their government positions, titles, or other authority the products, services, or activities of nonfederal entities .”

In the interview, Mr. Bridenstine acknowledged that federal employees are generally not allowed to endorse products, but said the committee would explore possible exceptions that would allow NASA astronauts to do so. He noted that soon there will be astronauts employed by commercial companies like SpaceX and Boeing who will not be fettered by the traditional restrictions that apply to federal employees.

The military has trouble retaining pilots who can earn more and work less flying commercial jetliners, he said. “We could end up spending millions of dollars training each astronaut only to have them go work for someone else as soon as they’re trained,” he said.

Because NASA does not operate the rockets going to the space station, the agency might not get a cut of the branding revenue, but the rocket company could then make a lower bid on what it charged NASA, Mr. Bridenstine said. The cargo missions are operated, under commercial contracts with NASA, by SpaceX and Northrop Grumman.

The committee is likely to make recommendations at the next quarterly meeting of the NASA advisory council, he said.