It is part of a drive towards "commercialisation", seen by its backers as a way to bring down the costs of space exploration while boosting efficiency.
However, the embrace of the private sector has created a backlash among some former astronauts, who likened the proposals to the sound of "nails on a chalkboard".
Bridenstine, the Nasa administrator, floated some ideas for how commercialisation could work at a meeting of the Nasa advisory council last month.
He said: "Is it possible for Nasa to offset some of its costs by selling the naming rights to its spacecraft, or the naming rights to its rockets?"
He added: "I'd like to see kids growing up, instead of maybe wanting to be like a professional sports star, I'd like to see them grow up wanting to be a Nasa astronaut, or a Nasa scientist.
"And so how do we make that a reality?... I'd like to see, maybe one day, Nasa astronauts on the cover of a cereal box, embedded into the American culture."
A Nasa source told The Daily Telegraph that the drive behind commercialisation included creating "excitement, interest and involvement" as well as bringing in money.
The Nasa Saturn V rocket is a huge attraction at the Houston Space Centre. Photo / AP
Some former astronauts appear unimpressed, criticising the ideas in comments made to The Washington Post, the newspaper that first reported the developments.
Scott Kelly, one former Nasa astronaut, said that the changes "would be a dramatic shift from the rules prohibiting government officials from using their public office for private gain".
Michael Lopez-Alegria, another former Nasa astronaut, told the paper: "It's going to be really hard for Nasa or any government agency to put itself in a position where it can become a de facto endorser of this product or that product. To me, it's like nails on a chalkboard. It's just not right."
Branding attempts in space are not entirely new.
Pizza Hut once painted its logo on a Russian rocket in 1999, while an Israeli milk company filmed an advert on the space station Mir.
