Should they sign the deal, the actor will play a married father who has since become known as the Angel of Death while the actress will portray a medical colleague.
Oscar winner Eddie Redmayne is in talks to portray a murderous nurse in a real-life thriller opposite Jessica Chastain.
Both actors are close to signing on for The Good Nurse, which will chronicle the efforts to hunt down Charlie Cullen, a notorious serial killer who was captured in 2003 and confessed to taking the lives of up to 40 patients in New Jersey and Pennsylvania over 16 years, starting in the late 1980s.
He was ordered to serve 18 consecutive life sentences for his actions.
Redmayne will play Cullen, a married father who has since become known as the Angel of Death, and Chastain has been tapped as the medical colleague who helped two former homicide detectives bring Cullen to justice after years of evading the law.
The film was adapted by Krysty Wilson-Cairns from the 2014 book The Good Nurse: A True Story of Medicine, Madness, and Murder, written by journalist Charles Graeber.
The project has been in development for at least two years, with Danish writer/moviemaker Tobias Lindholm signing on to make his English-language feature directing debut with the film in 2016.
Darren Aronofsky has also been involved in The Good Nurse for some time as it will be produced through his company, Protozoa.
If Redmayne signs on, it will mark quite the departure from his most recent role as Newt Scamander in the Harry Potter spin-off, Fantastic Beasts and Where to Find Them, and its upcoming sequel, Fantastic Beasts: The Crimes of Grindelwald.
He also starred as physicist Stephen Hawking in the biopic The Theory of Everything, a part which earned him the Best Actor Oscar in 2015.