Alexander Denk, who had worked as a bodyguard for Smith, told the television newsmagazine "Extra" that he had an affair with Smith, and that it's possible he is the father.
Denk's attorney, Cyrus Nownejad, did not immediately return a message from The Associated Press seeking comment. Ron Rale, a lawyer for Smith, also did not immediately return a message.
Prince Frederic von Anhalt said Monday he plans to file a paternity challenge to gain custody of Smith's infant daughter, even if it costs him his marriage to Zsa Zsa Gabor.
"If the court rules in my favor, I will go to the Bahamas and pick up the child," he said, adding that he would ask for a DNA test.
Smith's companion Howard K. Stern and her former boyfriend, Larry Birkhead, also have claimed paternity of 5-month-old Dannielynn.
Stern is listed on a birth certificate as Dannielynn's father.
The baby stands to potentially inherit a fortune from Smith's late husband, oil tycoon J. Howard Marshall II.
Von Anhalt, 59, and Gabor, 90, have been married for more than 20 years. The news of her husband's alleged affair has deeply upset Gabor, according to von Anhalt.
"She says, of course, 'If you bring a baby home then it's over,"' he said. "If my wife wants to divorce me then it's up to her."
There is also a claim from Smith's half-sister that Marshall may be the father. She claims Smith froze Marshall's sperm and may have used it to become pregnant.
