While the True Blood hunk, 33, and the 27-year-old actress have shown public displays of affection, they've never actually confirmed that they are a twosome.
They were recently spotted lunching at Doughboys in L.A. Our spy tells us that Skarsgård, lookin' all hot and stuff in a Levi's X Opening Ceremony T-shirt, "kissed Kate's hand" as she grinned ear to ear.
"They were laughing all throughout lunch and looked cozy on a date," the source adds.
Do think it's time for Skarsgård and Bosworth to come out of the coffin closet as a couple? Leave your comments after the jump, where you'll also find scoop on Kim Kardashian, a surprise birthday party for a Twilight star and so much more...
B-DAY GIRL: Ashley Greene, being surprised by friends Jonah Hill and Jessica Szohr with a belated birthday party at L.A. nightclub Trousdale a few nights before Lindsay Lohan and Leonardo DiCaprio were there chatting up Hollywood nightclub guru Woody Woodbeck.
MUSIC MAN: DiCaprio, continuing to get his party on at Rockjazz pianist ELEW's gig at L'Ermitage hotel in Beverly Hills.
POOL & PALS: Clash of the Titans stud Sam Worthington, playing pool and enjoying martinis with friends at Lola's in West Hollywood.
OH, BABY: Jennifer Hudson visiting fiancé, David Otunga, with their son, David Jr., backstage at Wrestlemania 26 in Glendale, Ariz.
WORK IT OUT: Jack Black, working out at Equinox gym in West Hollywood.
DATE NIGHT: Dave Matthews, dining with wife Jennifer and friends at the Vanderbilt in Brooklyn.
MUSIC OF THE HEART: Usher and Mandy Moore are expected in the audience at rock band the Ruse's performance at the Global Initiative University Meeting hosted by Bill Clinton at the University of Miami in Coral Gables, Fla., April 16-18.
—Additonal reporting by Claudia Rosenbaum
We really need a photo of Alexander Skarsgård without his shirt on so we can include him in our smokin' Hot Bods photo gallery.