Inventors have until December 20 to submit designs for a personalised waste-wicking system that will handle everything, hands-free, for a period of up to six days.
According to the competition website, the current solution consists of wearing nappies.
"However, the diaper is only a very temporary solution, and doesn't provide a healthy/protective option longer than one day," the website says.
Astronauts need a solution to this problem that works for more than a day or two.
For instance, earlier this month the two men and one woman who packed themselves into a Russian Soyuz space capsule had to wait two full days between launching from Kazakhstan and arriving at the International Space Station before getting to use a toilet.
But on future missions to deep space destinations like an asteroid or Mars, NASA suspects it could take up to 144 hours, or six days, to get to a proper toilet.
The suits will also provide a much needed contingency plan for astronauts in times of crisis when getting to the space station or back to Earth will take a long time. In emergency situations, astronauts may need to zip themselves into a fully pressurised, bulky orange spacesuit, complete with helmet and gloves.
"While sealed, it is impossible for an astronaut to access their own body, even to scratch their nose," NASA said.
And of course, the problem is that in weightlessness, fluids can blob up and stick to surfaces, while solids float in the air.
"You don't want any of these solids and fluids stuck to your body for six days," NASA said, recalling how easy babies can get diaper rash.
Currently, while at the International Space Station, astronauts use a toilet contraption that includes a vacuum and a tube to help evacuate faecal matter.
To urinate, they use a funnel attached to a hose that can be adapted for a sitting or standing position, and uses air to move urine away.
So if you've been ruminating on a solution for the space poop challenge and want some extra cash, at the time of writing you have 23 days left to enter the competition.
NASA will choose three winning concepts and the goal is to test them within a year and fully implement them within three years.