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."
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."