The laboratory has already received some cells from the dog, which is part collie, part Alsatian, Newsnight said on Monday.
The cloning laboratory of Texas A & M University at College Station had been given two years to produce a clone.
Laboratory Director Mark Westhusin said he thought other millionaires would be keen to follow suit.
``I'm sure there are lots of them out there that would if they knew the potential existed to do it,'' Westhusin said.
Newsnight said other laboratories and companies were hoping to move into commercial cloning of pets and racehorses.