Trakr, a German shepherd who lives with his owner, James Symington, in Los Angeles, has been chosen for the procedure by a Californian company.
BioArts International said the dog was the most "clone-worthy" canine in a competition offering an owner a free chance to replicate their pet.
Mr Symington said he and Trakr were among the first search and rescue teams to arrive at Ground Zero after the 2001 terror attacks that left about 3,000 people dead.
Together, they were responsible for locating the last human survivor under about 30ft of debris.
Now aged 15, the dog no longer has the use of his back legs due to a degenerative neurological disorder.
According to BioArts, experts believe the condition may be linked to exposure to toxic smoke at the World Trade Center site.
Mr Symington said: "Trakr means the world to me.
"To know that part of him is going to live on is just beyond words. It's the greatest gift I've ever received."
In the next month, BioArts said it would transport a sample of Trakr's DNA to the South Korean lab of its partner, the Sooam Biotech Research Foundation, and that the clone could be ready by the end of this year.
South Korean experts have been cloning dogs since 2005.
In February a company in the South East Asian nation said it was offering the world's first pet cloning service.
Although cloned animals look like their predecessor, experts say their behaviour will not necessarily be the same - meaning there is no guarantee that Trakr's clone will be quite as courageous.
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