Romance rumor du jour: Which actor may be smitten with Katie Holmes?

It's a tradition that dates back to the earliest days of showbiz: When you have a project to promote, stir up a little romantic intrigue. For Katie Holmes, whose new Broadway show, "Dead Accounts," begins previews this week, that means rumors about a supposedly smitten castmate.

The New York Daily News says the former Mrs. Tom Cruise has a "not-so-secret admirer" in co-star Josh Hamilton (that's him on the left). A source claims that he's "really crushing on her and is making that clear to her every opportunity he gets. He's always nearby, in her face, during lunch, [and during] breaks."

That's probably not the best way to befriend a woman who supposedly had to use disposable cell phones to plot her divorce due to alleged day-to-day scrutiny by Cruise and his minions.

Anyway, Us also plays up the ostensible connection. In a story headlined "Katie Holmes Bonds With Broadway Costar Josh Hamilton Post Superstorm Sandy," the mag notes that the two hung out last Thursday during a break in rehearsals.

Hamilton, 43, however, has been with actress Lily Thorne since 2005, and a source tells Gossip Cop that he "adores" her. They are reportedly expecting their second child.

A rep for Holmes, 33, who recently shot down rumors linking her to actor Alex Schemmer, laughed off the romance rumblings. For now, the actress appears to be concentrating only on 6-year-old Suri and her work.

"She's really focused on her career and Suri right now," a source tells the paper. "She spends a lot of time at rehearsals, with her daughter, and at the gym. And that's basically about it. She'll get back to dating sooner or later. But it'll probably be later."

Keep clicking for recent pics of Katie, who waited out Sandy in her Chelsea apartment with Suri before moving to a hotel when they lost water and power …