The plan is being seriously considered and the US has discussed the matter with Libya's leadership, according to the American media company's sources.
In exchange for the Palestinians, the US would release several billion dollars to Libya, money that the US froze over a decade ago.
Libya has been plagued by instability for nearly 14 years, since a civil war broke out in the country and the long-time dictator Muammar Gaddafi was overthrown.
"Ready to fight"
The high-ranking Hamas representative, Basem Naim, says that the movement is not aware of any discussions about moving Palestinians to Libya.
The Palestinians are very rooted in their homeland and very strongly engaged in their homeland. They are ready to fight to the end and to sacrifice whatever it takes to defend their homeland, their families and their children's future, says Naim, who is part of the terror-listed Hamas political wing, to NBC News.
(The Palestinians) are exclusively the only party that has the right to make decisions for the Palestinians, including Gaza and the Gazans, what should be done and what should not be done, he adds.
Would require 1,000 flights
Exactly where in Libya the displaced Palestinians would be moved to has not been determined, according to NBC's sources. It is also unclear how they would practically get from the Gaza Strip to Libya.
It would, for example, require approximately 1,173 flights with the world's largest passenger plane, Airbus A380, with maximum passenger capacity to transport one million people, the media company writes.
Since there is no airport in Gaza, it would first require transportation to an airport in the region to transport anyone from there by air.
