And he addressed a claim from Trent Bolte, a 29-year-old man from Wyoming, that the pair dated for almost a year.
In the recording, an investigator can be heard telling Watts that there have been “so many people who claim to have been with you, dated you and slept with you”.
The killer said his lawyer told him about “some dude from Wyoming” and that the story “blew my mind”.
“I was like, who the hell is this guy?” Watts said.
After Watts’ crimes gained global attention last year, Mr Bolte came forward to the media — initially anonymously, before sitting down for an on-camera interview — to claim they had started chatting on a dating app in 2017 before beginning a relationship.
“He said he didn’t know if he was bisexual or gay,” Mr Bolte told Inside Edition.
“Chris said that he was in love with me. He said he had never been so comfortable with someone. He said he felt like he could actually be himself around me.”
He showed the program text messages, which he says were from Watts, including one that said he missed his face.
While he knew Watts had a family, Mr Bolte said he had the impression his apparent lover had split from his wife. When he found out they were living together, he confronted Watts.
“I said, ‘Why don’t you just file for divorce?’ He said, ‘I’m just worried that she won’t let me see the girls,’” Mr Bolte said.
He claims they split up in May last year, just months before Watts murdered his family. He blamed Watts’ “lies” for the end of the relationship.
In the interview with police last month, Watts denied he had ever met Mr Bolte. He also disputed claims he would travel to see him.
“I’ve never even been to Wyoming, let alone driven there to meet a person,” he told investigators.
“I’ve never met the guy … I have no clue who the guy is.”
In his own interview with police late last year, Mr Bolte said the pair had communicated via the text messaging service WhatsApp.
Watts said he had never heard of the application nor downloaded it on his smartphone, which police have in their possession.
The killer revealed that his lawyer had also told him about a second man who claimed they had had a gay relationship.
The man claimed to have met Watts in a rehabilitation facility, which he denied.
In the interview, an investigator asks repeatedly if Watts has ever had any gay experiences, any interest in men or at any time wondered about “experimenting”.
“No,” he flatly answered.
Mr Bolte has denied earlier media reports that he worked as a gay escort when he met Watts, although claimed he was given money — including for cosmetic beauty treatments like Botox and lip fillers.
Since coming forward and Mr Bolte said he has been attacked by online trolls about his claims and his appearance.
On August 31 last year, he took to Twitter with an ominous post, saying: “I just want to crawl under a rock, I’ve never felt so overwhelmed.”
Shortly after, he posted a selfie to Instagram with a caption saying his “mind is racing and it won’t stop”.
“I haven’t got a good nights sleep after hearing that terrible news,” Mr Bolte wrote.
“Social media has drug me thru the dirt and back because the media getting hold of picture of me, releasing my name on record. The trolls of social media have called me a fudge packer, he/she/it, the f word, homo, anything you can think of but I’m trying to rise above it.”
A report of a police interview with Mr Bolte’s mother, Colleen, has also been released in which she reveals her son told her about Watts long before “the horrible crime”.
Mr Bolte told her about a relationship he was having with “a man named Chris (who) visited from Colorado”.
In the prison interview, Watts was also asked about another person who came forward to the media claiming to have had a sexual affair with him — a woman named Amanda McMahon.
She said they had “a rendezvous” in the car park of the fast food restaurant Chick-Fil-A, but he denied having met her.
But Watts did go into detail about his affair with a colleague, Nicole Kessinger, who he was in a relationship with.
He provided information about how their relationship began, his regrets in hindsight and how she had nothing to do with the murders.
And Watts revealed that he and Shanann had sex just hours before he put his hands around her neck and strangle her.
Watts told investigators on the morning of the murders, he and Shanann were having an argument in their bedroom, during which he admitted he had been having an affair.
He said his wife had started crying and saying, “I knew there was someone else” and, “You’re never gonna see the kids again.”