The pair are in line to appear in Bigelow's first film since 2017 although details about what characters they will be playing are yet to be revealed.
News of the untitled movie was first disclosed by Netflix during its Upfront Presentation in New York recently and sources say that it will be set at the White House during an unfolding national crisis.
Bigelow - who became the first female to win the Oscar for Best Director for her work on the 2008 movie 'The Hurt Locker' - had been due to helm an adaptation of the novel 'Aurora' for the streaming giant but it ultimately failed to get off the ground.
Idris has long been tipped to succeed Daniel Craig as James Bond and joked earlier this year that he is now "more famous for not playing" 007 than past actors who have portrayed the spy.
Speaking to Radio X, the 51-year-old star said: "It was definitely one of the biggest rumours. I'm arguably more famous for not playing Bond than some of the actors who did!
"And you know, it's been one that I've taken lightly at times. You know, everyone loves Bond. Such a fantastic character, and just to me, I found it as a compliment to be considered all those years ago."
The 'Hijack' actor previously accused racist trolls of putting him off wanting to don Bond's tuxedo.
Idris told the 'SmartLess' podcast: "Essentially, it was a huge compliment that every corner of the world except from some corners, which we will not talk about, were really happy about the idea that I could be considered.
"Those that weren't happy about the idea made the whole thing disgusting and off-putting because it became about race. It became about nonsense, and I got the brunt of it."