Suleman confirmed that while dating Denis Beaudoin from 1997 to 1999 she twice tried to become pregnant with him through artificial insemination but was unable to conceive.
The octuplets and her six older children were all conceived using one other man's sperm, she said through a spokesman.
"Absolutely, Denis is definitely not the father," said Suleman's spokesman Victor Munoz.
Munoz said Suleman, 33, was "absolutely willing" to submit the children to paternity tests, and that he had been trying "to get a hold of Denis all day and yesterday" to arrange testing.
On Monday, Beaudoin told "Good Morning America" that he donated sperm on three occasions in the late 1990s, and he believed he could be the children's father.
Munoz called the offer Beaudoin made on "GMA" to help raise the children, even if he is not the father, a ploy to reignite a relationship with Suleman, but the mother of 14 is not interested.
"He wants a relationship with her, and she doesn't want a relationship with him. They broke up for a reason," Munoz said.
Twice, he said, he gave Suleman a sperm sample at home, which she held between her breasts to keep warm. The third time, he said, he was brought to a fertility clinic after Suleman told him she had cancer and they were going to see a doctor.
"When they were a couple they tried to conceive a child. They were in a relationship and wanted to have a child together," said Munoz, who confirmed Beaudoin gave two samples at home.
According to Munoz, Suleman was artificially inseminated with Beaudoin's semen and no embryos were created for implantation. He said all of the sperm was implanted at the time and none remained to be used at a later date.
"The sperm was placed [directly in her womb]; it wasn't turned into an embryo and then placed. There isn't anything left over. It was all planted in the hopes it would work. It was the easier, cheaper version at the time and it didn't take," the spokesman said.
Munoz said all 14 of Suleman's children have one father, but that "the real father doesn't want to come out. That's just the bottom line."
Munoz said that while Suleman and Beaudoin were dating, she was married but separated from Marcos Gutierrez.
Suleman divorced Gutierrez in January 2008. According to divorce documents filed with the San Bernardino Superior Court, there were "no children of the marriage," suggesting that Gutierrez was not the father of Suleman's previous six children.
A review of birth records by The Associated Press identified a David Solomon as the father of the oldest of the four children.
Munoz said there was one father for all the children but would not confirm his name.
Suleman made headlines in late January when news that she delivered eight viable babies was heralded as a medical marvel.
In the days that followed the Jan. 23 delivery, critics raised a host of questions about the ethics of artificially implanting a woman with so many embryos, and a single mother's ability to financially support 14 children.
Suleman is unemployed and lives in a three-bedroom home with her parents, who have publicly criticized their daughter's decision to have so many children.