CBS News Entertainment Contributor Jill Dobson reported Monday production is slated to begin on just after Labor Day.
Who will she be?
The actress hasn't been announced yet, but Dobson said word is expected any day now, with movie executives reportedly looking for an unknown for the part.
Dobson pointed out the part played by Swedish actor Noomi Rapace in the European original is set to become the hottest movie role in recent history.
As Pat Saperstein, senior editor of Variety, told CBS News, "It's just this really interesting role that's going to continue for two more films. So really, it's like a trilogy of projects for a young actress that could really make an actress's career."
Director David Fincher, who broke out with the runaway hit "Seven," has found a leading man in Daniel Craig of James Bond fame. But rumors are rampant about his co-star. Dobson reported it's rumored actresses Natalie Portman and Ellen Page may have a shot at the tattooed and pierced female lead.
Pictures: Natalie Portman
Picture: Ellen Page
However, some fans of the books, such as Ian LaFrenais, hope the lead casting isn't in the Hollywood vein.
"I hope not a well-known girl," he told CBS News. "I hope it's someone new and startling."
As for Craig's love interest in the film, Robin Wright is reportedly going to play Erika Berger.
Pictures: Robin Wright
"Early Show" anchor Erica Hill said it it's interesting that people are hoping to have an unknown play the lead.
Dobson said the casting is similar to the "Twilight" series of films, in which several unknowns became known because the franchise was so popular.
"The Girl with the Dragon Tattoo" movie is based on the book by Swedish investigative journalist Stieg Larsson, the first in a trilogy of crime thrillers that have become a worldwide phenomenon. A movie has been released in Europe and 40 million books have been sold around the globe. Larsson is one of the first authors to sell more than a million e-books.
Larsson died of a massive heart attack at age 50 before his now best-selling novels were ever published.