The gossip blog, Celebrity Dirty Laundry, claims to have learned of the affair through an unidentified source.
"A source exclusively told CDL that David and Gillian have been in a serious relationship for some time now and she and her children are shacking up with the 'Californication' actor," claims the site. "This is a long time coming for the pair whose chemistry on their hit show was always a source of tabloid conjecture."
Anderson and Duchovny costarred on "The X-Files" from 1993 to 2003. Each has had their fair share of failed relationships: Anderson split from husband Clyde Klotz in 1997 after four years of marriage. The 44-year-old then married Julien Ozanne in 2004,and the two divorced in 2006.
Duchovny, 52, married actress Tea Leoni in 1997. The couple separated in 2008 while the actor underwent treatment for sex addiction, but appear to have later reconciled -- temporarily. While some reports allege that their marriage ended in 2011, they have yet to announce their divorce.
"After all these years, we want to believe they're a couple, but the website's 'evidence' that the pair are romantically involved is paper thin," concluded the Huffington Post.
On Thursday, Celebuzz obtained an exclusive statement from Duchovny's rep who said that the reports of an "X-Files" romance are "not true."
Celebrity Dirty Laundry did not immediately respond to an inquiry. Regardless of the truth behind the rumors, Gawker believes that the chatter, which has left "X-Files" fans overjoyed, is harmless.
"Even if untrue, these rumors aren't really hurting anyone. Both Anderson and Duchovny split up from their longtime partners - Anderson broke up with boyfriend Mark Griffiths recently, and Celeb Dirty Laundry claims Duchovny and Tea Leoni have been 'quietly divorced' for the past three years."
Indeed, who can resist the idea of onscreen chemistry turned real-life romance? Here's hoping the rumors aren't entirely science fiction!