The 33-year-old actor is in discussions about a role in John Logan's 'Double Feature', a pair of plays which would also star Anne Hathaway.
and his former 'Game of Thrones' co-star Conleth Hill.
Kit is in talks for the second part of the productions, which follows a young man who idolises horror icon Vincent Price, only to find reality is very different when he comes face-to-face with his hero, the Daily Mail newspaper's Baz Bamigboye has revealed.
The 'Devil Wears Prada' actress is to portray Tippi Hedren in the first play, which will explore the toxic relationship between the 'Birds' star and her director Alfred Hitchcock. Conleth is in line to play the legendary filmmaker.
'Double Feature' is being written by 'Penny Dreadful' creator John Logan and will be directed by Jonathan Kent, while 'La La Land' producer Marc Platt is on board to produce.
The production is still in its early stages, but is planned to start in New York next year and if it proves a success, there are plans for it to later transfer to London's West End.
Meanwhile, Kit recently admitted he has found it very "freeing" to voice Eret in two 'How to Train Your Dragon' films because playing Jon Snow in 'Game of Thrones' was very "restricting".
He said: "That's a great gig. You rock up in your pyjamas. I'm going to make it sound easy but it is not. It is not easy. They find you wherever you are in the world. Cause you can record it in any recording studio. They can Skype in, and the director can direct you that way.
"Honestly it's very freeing. I loved it. For many years playing Jon Snow, who is swaddled in dead animals. For him, it can be very restricting. In this voice work, you are free to do whatever you want. You can go crazy and the crazier you go, the better it is. You can create more of a character I guess. So, I'd love to more voice work, it's fun."