The film is slated to star Leonardi DeCaprio, who will also co-produce it, alongside his long-term business partner Jennifer Davisson.
According to Deadline.com, the deal is worth more than $500,000.
The book, the first to be written under Nesbø's new pseudonym Tom Johansson, is about a hit man who falls in love with the woman he is contracted to kill.
The novel was sent out to film production companies on Friday by Nesbø’s agent Sylvie Rabineau.
It will be published in America next spring through US publishers Knopf, with a sequel, More Blood On The Water, scheduled for the following year.
According to the website the third book in the series, The Kidnapping, will see Tom Johansson, Nesbø's new pseudonym, kidnapped and himself become a character.