The woman, who identified herself as "cousin Pebbles," added, "He's been gay since he was probably five."
Over the weekend, Rimes' rep issued the following response to reporters.
"Although Dean and LeAnn never knew they had a cousin named Pebbles, they are glad to hear that she has come out of the woodwork," he said. "Dean and LeAnn are also interested in connecting with their other long lost family members: Fred, Wilma, Barney and Bamm-Bamm. So Pebbles, please let us know if you have spoken to them, too."
Beyond that, Rimes' rep refused to comment on her client's personal life, which is newly in the spotlight because of an Us Weekly report that the country music prodigy, 26, is having an affair with Cibrian, 35, her co-star in the Lifetime movie "Northern Lights," which premiered Saturday night. While ratings information for the premiere was not immediately available Sunday, speculation about whether Rimes and Cibrian's love scenes might appear a bit more authentic than normal is likely to have brought Lifetime a big audience.
Us Weekly is citing as proof security camera images of the couple making out during an intimate dinner and photographs of them arriving at and leaving an exclusive Beverly Hills hotel, where they allegedly had a four-hour rendezvous.
"She is having an affair," senior editor Ian Drew said. "It's not even a joke or speculation or from a shady source."
But why put Rimes, whose biggest hit "How Do I Live" was back in 1997, and who has been overshadowed by current country-music princesses Taylor Swift and Carrie Underwood, on the cover?
"Everyone thought she had this perfect marriage, she always had such a perfect reputation," Drew said. "It's just a surprise to everyone."
After the story of their alleged affair broke on Tuesday, Cibrian, who is married to model Brandi Glanville and the father of two boys, released a statement, which ABCNews.com obtained:
"Other than being friends and two actors who were romantically intertwined in a movie-for-television we filmed last fall, there is no truth to the reporting initiated by Us magazine. It is a fabricated story that is using random snapshots as connective tissue to create a scandalous relationship."
Rimes, married seven years to aspiring songwriter Dean Sheremet, responded to the report in a blog post on her Web site. But she left readers with plenty to read into:
"This is a difficult time for me and my loved ones, but I appreciate all your continued support. I would like to assure all of you that this is a place for you to hear things directly from me and as you all know, not everything in our lives is always black and white. Have faith, Le."
More Than Black and White
Later on Wednesday, when she appeared on "Live with Regis and Kelly," Rimes didn't exactly put rumors to rest.
"Everything's great. There's rumors all the time," she said. "Things pass, life happens. You know, everything people read is not ... as easy as black and white. That's what it is. I let it roll off my back most of the time."
"Even if she did deny it, she would look like a liar," Drew said. "These are real photographs. She's on video making out with him. She can't deny it. It happened. There are no ifs."
The magazine said the couple's affair began March 7 with a romantic lunch at the restaurant Mosun and Club M. in Laguna Beach, Calif. They held hands, laughed and kissed throughout their dinner.
Then on March 14, Rimes was spotted sans wedding ring carrying a copy of the book, "For Better or for Worse: Divorce Reconsidered." Later that day, Us Weekly said she checked into a $725-a-night suite at the Malibu Beach Inn. An hour later, Cibrian pulled into the parking lot and headed for Rimes' room. They remained inside with a "Do Not Disturb" sign on the door for more than three hours before leaving separately.
Rimes and Cibrian, who has appeared in episodes of "Samantha Who?" and "Ugly Betty," first met on the set of their television drama "Northern Lights," in which she starred as an Alaskan bush pilot who fell for the new detective in town, played by Cibrian. Through the shoot, which included some steamy love scenes, they became close.
The director Mike Robe told Us: "From the moment we rehearsed, LeAnn and Eddie honestly developed a really strong bond and a warm relationship. I could sense a lot of trust that grew between them. Once I yelled 'cut,' they did have a rapport. They became very good friends."
Various media reports say Rimes' marriage has been in trouble for some time, a product of getting married too young. Rimes wed former backup dancer Sheremet when she was 19.
A friend of the couple told People magazine: "Like any marriage, they've had a couple of rough patches. They've gone to therapy. But they did marry very young and when people marry young it's very difficult to maintain a marriage for the long haul."
Will Rimes' Marriage Survive, Career Thrive?
Sheremet, 28, who has been working in Nashville as a songwriter, twittered about his wife Thursday amid the swirling rumors. "I love my wife!!!" he wrote.
"I'm sure he does," Drew responded. "What's he going to do. He has no other career. He's married her."
Celebrity blogger Perez Hilton, who claims that Sheremet acts as Rimes' current stylist, questioned his sexual orientation.
But Drew said sources close to Rimes told the magazine that, "He's not gay and very secure in his sexuality."
The couple's friend told People: "[LeAnn and Dean] are figuring it out. They have a lot of mutual respect for one another."
As for Rimes, who moved from Nashville to Hollywood last year in an effort to reboot her career as an actress, making the cover of Us may not be such a bad thing, Drew said.
"I think this is a boost to her career," he said. "Where was it really? She hasn't had a hit in a while, she's doing a Lifetime movie. This is more press than the movie would have ever gotten."