The space agency is planning to offer help to the California resident, Mr. Milner, in the first private mission in deep space, a journey in the intriguing but small moon millions of kilometers away beyond the asteroid belt, according to the New Scientist magazine.
Agreements signed by NASA and the Milner Non-profit Breakthrough Starshot Foundation in September, as seen by New Scientist, reveal that the two organizations are working on ambitious mission scientific, technical and financial plans.
NASA has already committed more than £ 54,000 ($ 70,000) that will be spent on a concept study for a flyby mission.
The breakthrough will not be paid in cash – rather, the figure represents the personnel costs of the project agency.
The teams will come together to work on the plan and concepts of the project during the next year.
The icy moons that orbit around Saturn and Jupiter have emerged as significant places to look for life.
Europe, one of at least 69 moons orbiting around Jupiter, is often cited as the best candidate for searching for organisms living outside our planet, largely because it almost certainly has a huge undersea ocean.
The space agency is convinced enough that it is planning two multi-billion dollar missions to explore the frozen planet in the next decade.
And Titan, the largest of the moons of Saturn, which has a dense, nitrogen-rich atmosphere, is sometimes said to be similar to the Earth billions of years ago.
However, speaking at the National Geographic Explorers Festival in 2018 in July, NASA planetary scientist and consultant Carolyn Porco said that Enceladus was an even better candidate.
He explained: "I have an injury, and I do not deny it.
"But it's not so much an emotional attachment to the objects we study, it's a evidence-based point of view.
"We simply know more about Enceladus.
"Really, the people of Europe do not know much about it.
"There is a lot of excitement, but it is a speculation at this point, of course I would choose Enceladus."
Like Europe, Enceladus, which measures only 310 miles (500 km), also has a sub-shallow ocean – and a study published in the scientific journal Nature at the start of this year has identified large organic molecules spat in space from the inside as proof that the moon was a suitable environment for life.
The Breakthrough Initiatives project aims to answer the biggest questions about space, including if there is life on other planets.
His advice includes Mr. Milner, Facebook founder Mark Zuckerberg and Professor Stephen Hawking until his death in March.
The missions listed include a solar sail spacecraft to reach nearby stars, develop technology to find Earth-like planets, and send a message to extraterrestrials.
New Scientist reported that the Breakthrough Foundation, not NASA, would fund the Encelado mission.