"It is a fabricated story that is using random snapshots as connective tissue to create a scandalous relationship," Cibrian says in a statement first obtained by Access Hollywood.
A Rimes friend tells PEOPLE the country star, 26, and Cibrian, 35 – who is married to model Brandi Glanville and has two sons, Mason, 5, and Jake, almost 2 – are not in a relationship. "There are some feelings there but it's too early to tell if it's going to develop and if she's done with her marriage," says the pal.
While it's unclear how the allegations will affect Rimes's seven-year marriage to songwriter Dean Sheremet, the couple have definitely hit a rough patch, Rimes's friend confirms.
"[LeAnn and Dean] are figuring it out," says the friend. "They have a lot of mutual respect for one another."
"The situation that she's grappling with right now is not the cause for her marriage troubles," the friend continues. "There have been issues brewing for months prior to meeting Eddie on set."
Marrying YoungOne of those issues: getting married at such a young age (Rimes was still a teenager when she and Sheremet tied the knot). "Like any marriage, they've had a couple of rough patches. They've gone to therapy," says the friend. "But they did marry very young and when people marry young it's very difficult to maintain a marriage for the long haul."
After spending the first half of March apart – Rimes has been in L.A. doing voiceovers for her Lifetime movie Nora Roberts' Northern Lights, while Sheremet, 28, has been working as a songwriter in Nashville – the couple spent time together in Washington, D.C. on March 11 where they lobbied House and Senate members on behalf of a new bill to increase funding for psoriasis research (Rimes has suffered from the skin condition since the age of 2). Rimes and Sheremet are both currently in New York City, where she is promoting her TV movie.
Rimes met Cibrian on the set of Northern Lights, which filmed in Calgary last November and December and co-stars Rosanna Arquette. It airs on March 21.
Cibrian and Rimes play love interests – he's a former Baltimore cop who moves to a remote Alaskan town and falls for Rimes's character, a feisty bush pilot, when he investigates her father's death.
Additional reporting by LISA INGRASSIA