The video, including footage of Apollo 11 astronauts Neil Armstrong and Buzz Aldrin walking on the moon, was transmitted from the moon to tracking stations in the US state of California and Australia.
But the images that were then sent to Houston - and seen by the rest of the world - were substantially degraded.
Space programme veterans believe the original tracking station recordings are stored somewhere at Nasa's Goddard Space Flight Center in Greenbelt, Maryland.
However, Nasa officials said that despite the uncertainty they were confident the tapes had not been lost.
"The tapes are not lost as such, which implies they were badly handled, misplaced and are now gone forever. That is not the case," John Sarkissian, operations scientist at the Parkes Radio Observatory in Parkes, Australia, told the Space.com website.
Sarkissian also rejected any suggestion of wrongdoing on the part of Nasa.
"The archiving of the tapes was simply a lower priority during the Apollo era," he said.
"It should be remembered that, at the time, Nasa was totally focused on meeting its goal of putting a man on the moon and returning him safely to the Earth."
In a paper published in May, Sarkissian wrote that the use of digital processing techniques on the tapes would make it "possible to recover the original high quality television [pictures] of the first lunar EVA [extravehicular activity] and make it available to the public for the first time."