The anonymous Texan tycoon has engaged the cloning expert Dr Mark Westhusin - Director of Cloning at Texas A&M University - to create an exact replica of his beloved Alsatian-Border Collie cross called Missy.
Dr Westhusin, who has temporarily broken off his research into cattle cells in order to concentrate on cloning Missy, suggested that pet cloning is a growth industry.
"If you look at how attached people are to pets, this is not an unusual situation.
"I'm sure lots of them would clone pets if they knew the potential existed," he said.
British scientists recently pioneered a relatively simple technique to produce Dolly the sheep, the world's first "man-made" clone of an adult animal.
DNA from the animal to be cloned is injected into an egg cell from which the nucleus has been removed. The cell then "reads" the DNA to create a second animal that is an identical copy of the original.
Two new pet cloning companies are known to have recently opened in the US, including an Internet-based firm called Clonapet.
Clonapet claims to have DNA from more than 15 cats and dogs stored in special freezers and waiting to undergo the cloning process.
Professor of Genetics at Princeton University, Lee Silver, believes Dr Westhusin's research brings scientists closer to cloning people.
"The incredible thing is that if you can perfect the technology in lots of different animals it makes it that much more likely it's going to move to human beings," he said.