The 'Fantastic Beasts and Where to Find Them' actor is said to be lined up to play real life serial killer Charles Cullen in the big screen thriller - which Krysty Wilson-Cairns will adapt from Charles Graeber's book of the same name.
As reported by Vulture, 'Molly's Game' star Chastain will star opposite him as a fellow nurse who helped track down the murderer after he took the lives of as many as 40 patients before his arrested in 2003.
Darren Aronofsky's Protozoa Pictures has had the movie in production since 2016, and it appears there is finally movement when it comes to pulling a cast together.
Bron Studios will product the project, and release it through Lionsgate, while Danish filmmaker Tobias Lindholm has been attached as director for the past two years.
Meanwhile, Redmayne has been busy working on 'Fantastic Beasts: The Crimes of Grindelwald' - the sequel to the 2016 blockbuster - as he reprises his role as magi-zoologist Newt Scamander, and he recently revealed that the second film takes the series down a much more ''cryptic'' route.
Speaking about the movie - which is a spin-off of the 'Harry Potter' franchise - Eddie said: ''The most riveting aspect is the tonal change. It's darker and more rigorous and weaving in the 'Potter' lore we're much more familiar with.
''So these characters you met in the first film are now in the wizarding world you understand more thoroughly. When I read [the script] it had these cryptic elements to it and it played like a thriller that made it a page-turner.''