As Kotaku points out, Sony Pictures now holds the rights to bioshock-movie.com, bioshock-movie.net and bio-shock.net. None of those URLS bring up any sort of content, suggesting a preemptive move to lock up the domains in the event that Sony Pictures has need of them later.
While this does not necessarily mean that the BioShock movie has entered production, it should be mentioned that this isn't the first time we've heard about this project in recent months. An IGN report from March 13 claims that Courtnee Draper, the actress who lent her voice to BioShock Infinite heroine Elizabeth, has been badgering BioShock maestro Ken Levine for the same role in the event of a movie adaptation.
This is especially intriguing, given that Levine claims to have killed the BioShock production that Universal Studios was attempting to mount with Gore Verbinski in the director's chair. If Levine is still kicking around the idea to the extent that he's discussing the movie with a potential lead actress, maybe he hasn't entirely turned his back on the idea.
Our attempts to reach BioShock publisher 2K Games for more information were met with a boilerplate "no comment."