The 32-year-old actor looks set to star as Armstrong in the film which will focus on the seven-time Tour de France champion's long career and fall from grace after he admitted to taking performance-enhancing drugs, reported Deadline.
The movie is being written by "Trainspotting" scribe John Hodge, with production slated to begin this autumn.
Foster made his Broadway debut opposite Alec Baldwin in 'Orphans' last year and also stars with Mark Wahlberg in Peter Berg's "Lone Survivor".
Frears' intention to make a film about Armstrong's life comes as somewhat of a surprise since two other projects about the scandalous sportsman are already in the works.
Meanwhile, JJ Abrams is also hoping to bring Armstrong's tale to the big screen by adapting 'Cycle of Lies: The Fall of Lance Armstrong', a book by New York Times sports writer Juliet Macur.
Bradley Cooper was rumoured to be in line to play the cyclist, but he vehemently denied the claims.