This is from a couple of weeks ago, but I see that it hasn't been posted:

http://www.slashfilm.com/dragon-tattoo-sequel/

Rooney Mara thinks that the sequels are dead.

Maybe with the changes in Sony there will be a different situation, but I don't know, Fincher seems to be quite busy in the next months/years with tv projects and movies (Utopia, Strangers, etc), and I doubt that TR/AR would write the soundtrack if someone else was picked to direct the sequels.

I wish the whole team completed the trilogy (or tetralogy, since I read that Sony was going to buy the rights for another book that was written before the swedish author died), I liked Fincher's version better than the swedish film, and I've not seen the swedish sequels but I've read that they are not very good and were planned as direct-to-tv films that were also expanded and used as a tv series, with a much lower quality than the first one, also some people say that the books were not very good either, didn't read them, but Fincher was supposedly working with a script that changed a lot of things from the books, so I would love to see his vision of the sequels, but many years since the first movie will have passed once he has finished his other projects, I wouldn't be surprised if Sony hired a different director/team for the sequels if they are ever done.