The comet, according to scientists, started breaking up in August after being blasted by a huge solar storm, and most of it was finished off when it made a close pass by the sun last month.
So what will cruise within 22 million miles (35.4 million km) of our planet on Sunday is likely to be a stream of debris rather than a completely intact comet, they said.
"Folks (scientists) are having trouble finding it, so I think it's probably dead and gone," Don Yeomans of NASA's Near Earth Object Program Office was quoted as saying by SPACE.com.
That means it may not present much of a skywatching show on Sunday, he said.
According to scientists, Elenin's apparent demise may come as a relief to many, since apocalyptic rumours circulating on the Web portrayed the comet as a major threat to Earth.
One theory claimed Elenin would set off havoc on Earth after aligning with other heavenly bodies, spurring massive earthquakes and tsunamis.
Another held that Elenin was not a comet at all, but in fact a rogue planet called Nibiru that would bring about the end times on Earth. After all, the comet's name could be taken as a spooky acronym: "Extinction-Level Event: Nibiru Is Nigh."
Those ideas were pure nonsense, Yeomans said. "Elenin was a second-rate, wimpy little comet that never should have been noted for anything, really. It was not even a bright one," he said.
Elenin's remains will not be the only objects about to make their closest pass of Earth. One day after the Elenin flyby, the small asteroid 2009 TM8 will zip close by. Like Elenin, it poses no risk of striking our home planet.
Asteroid 2009 TM8 is about 21 feet wide and the size of a schoolbus. It will come within 212,000 miles of Earth -- just inside the orbit of the moon -- when it zips by on Monday morning (Oct. 17).
Elenin was named after its discoverer, Russian amateur astronomer Leonid Elenin, who spotted it in December 2010. Before the icy wanderer broke up, its nucleus was likely two to three miles in diameter, the scientists said.
According to Yeomans, Elenin never posed any threat to life on Earth. It was far too small to exert any appreciable influence on our planet unless it managed to hit us, he said.
"Just driving to work every day in my subcompact car is going to have far more of a gravitational effect on Earth than this comet ever will," Yeomans said.
Elenin's supposed connection to earthquakes was just a correlation, and a weak one at that, he added. Relatively strong earthquakes occur every day somewhere on Earth, so it's easy -- but not statistically valid -- to blame some of them on the comet's changing position.
Yeomans views the frenzy over Elenin as a product of the Internet age, which allows loud and often uninformed voices to drown out the rather more prosaic results that scientists publish in peer-reviewed journals. "It's time to move on to the next armageddon," he said.