The Hollywood stars have been eyed for the lead roles in the disaster drama film, inspired by the 1996 Mount Everest expedition which claimed the lives of eight climbers, reported Deadline.
Kormakur is attempting to gather up a star-studded cast and is considering handing the two other lead roles to John Hawkes - best known for 'American Gangster' and 'The Great Gatsby' actor Jason Clarke.
The film will focus on three disastrous attempted expeditions up Mount Everest in 1996 when a 'blinding' storm hit and killed a number of people, and producers will draw from a selection of books and interviews with survivors.
Brolin, who was recently seen in 'Gangster Squad', has four other projects in the pipeline, while Gyllenhaal's new thrillers 'Enemy' and 'Prisoners' are set to hit cinemas in the next few months.
Kormakur wants to start filming in November.