Jack Finney's illustrated novel follows a young illustrator who enlists in a secret government experiment, and is transported from the mid-20th century back to 1882 New York.
After he falls in love with a woman in the past, he is forced to choose between his old and new lives.
According to Variety, the project has been in the works for years and Robert Redford initially began developing it in the 1990s, having been introduced to the book by Paul Newman.
Liman's next project, the Tom Cruise-starring sci-fi All You Need Is Kill, was officially greenlit this week.
Watch the trailer for Liman's last film Fair Game below: