Doug Liman's film was set to star Hardy as British mountaineer George Mallory, who tried twice to scale Mount Everest during the 1920s before disappearing on the third attempt.
Deadline reports that scheduling conflicts have now forced Hardy to pull out, with Cumberbatch the frontrunner to replace him.
Several actors including Tom Hiddleston, James McAvoy, Henry Cavill, Matthew Goode, Dan Stevens and Joel Kinnaman are reportedly being considered to co-star as rival Australian climber George Finch.
Having failed to climb Everest in 1921 and 1922, Mallory and climbing partner Sandy Irvine vanished during a third attempt in 1924, and their bodies were not discovered until 1999. It is still unknown whether they had reached the summit before they died.
Cumberbatch is currently filming Alan Turing biopic 'The Imitation Game' alongside Keira Knightley.