Part of the reason for the new impetus – and right now, it's clearly still at discussion and theory stage – is the publication of a fourth book featuring hacker Lisbeth Salander, The Girl In The Spider's Web, which was written David Lagercrantz following Larsson's death in 2004 and looks set to kick Salander back into more public awareness.
But given the struggle to make the first film (there was much wrangling between Fincher and the studio), the thinking now seems to be a combo film of the other two books and then possibly an adaptation of Spider's Web after that. Nothing has been said about who might tackle the idea if it even goes ahead, so we shouldn't assume Fincher and cast members such as Rooney Mara (Salander) and Daniel Craig (Mikael Blomkvist) will return.
Worldwide, the first film took in $232 million on a reported $90 million budget, so there might not be the biggest rush here. But Sony could use all the recognisable properties it can round up, which means we shouldn't count Lisbeth out just yet.