The Lunar Loo Challenge - which could earn the winner £28,000 - comes as the organisation is looking to develop a new way for astronauts to use the bathroom ahead of a planned return to the moon by 2024.
Space toilets are already in use - with the International Space Station set for an upgrade - there are design for microgravity in the vent of weightlessness.
However, the new toilets must be able to work in lunar gravity - which is around one-sixth of the Earth's.
The strict regulations and specifications mean the new loo has to have a mass of less than 15kg in Earth's gravity, while taking up a volume no grater than 0.12 metre cubed.
Furthermore, it must consume less than 70 watts of power, operate with a noise level of less than 60 decibels, and be able to accommodate both male and female users of varying shapes and sizes.
Mike Interbartolo - project manager for the Lunar Loo Challenge in the HLS Crew Compartment Office at NASA's Johnson Space Center - said: "While we may know how to make space toilets, we recognise that there are a lot of innovations going in waste management from the no-flush toilet to waterless toilets and more.
"So we wanted to expand our knowledge base by using this challenge to find the unknowns that might be out there.
"We are looking forward to seeing what the crowdsourcing community can come up with that is out-of-the-box and bring different perspectives for what is needed for a toilet."