Christopher Nolan is at a point in his career when he could get pretty much any movie he wanted green-lit, just by showing some interest. Inception, a huge risk, paid off incredibly well for Warner Bros. and grossed in the region of $800 million worldwide; now the studio want him to tackle a new franchise.
According to Variety, Nolan is the man Warner want to direct a new Twilight Zone movie - with Michael Bay and (Rise of the Planet of the Apes director) Rupert Wyatt also being considered. Leonardo DiCaprio is producing the film, which is probably why Nolan's name is being mentioned. After only a handful of feature films under his belt, his name screams an almost Spielbergian level of possible box-office - and he's up there with the David Fincher's of Hollywood in terms of consistency. Whether he signs on or not is something else entirely as he doesn't seem keen on directing other peoples scripts - and there's already one for this remake/adaptation.
The original series ran from 1959-64, and was turned into a movie in the 80s with individual segments helmed by (amongst others) Steven Spielberg and Joe Dante. It was rebooted for TV again in 2002 after the global success of The X-Files, but didn't last long. Nolan is currently shooting the final film in his Batman trilogy, The Dark Knight Rises.