Sony Pictures and Escape Artists are looking to adapt the 1980s television series into a new feature film, reported Digital Spy online.
Refn, director of "Drive" and "Bronson", has been offered the chance to helm the new version.
Washington is attached to star, and the script has been written by Richard Wenk, who is currently working on the screen play for the live-action Masters of the Universe adaptation.
The original TV series starred Edward Woodward as Robert McCall, a former black ops agent for the government who attempts to atone for his shady past by offering his skills to those in need.
Refn has reunited with "Drive" star Ryan Gosling for the forthcoming "Only God Forgives", while Washington is rumoured to be a potential Oscar contender with "Flight", currently on US release and due out in the UK in February.
