The 'Captain Phillips' director will take on the story, which has been adapted for film from a book proposal by author Greg Mitchell, reported Digital Spy.
'The Tunnels' is based on the true story of a great escape before the Berlin Wall fell in 1989.
The story follows a group of West Germans trying to get their loved ones out of East Berlin, with the help of American news networks, which funded the expedition.
Mitchell announced the news via his website.
He wrote: "As my proposal for my next book 'The Tunnels' was purchased by great upstart company FilmNation for a major film directed by my one of my film heroes Paul Greengrass."
Greengrass has been linked to the new 'Bourne 5' film after departing the franchise after 2007's 'The Bourne Ultimatum'.
New star Jeremy Renner has recently said he'd like Paul Greengrass and Matt Damon to return to the 'Bourne' films.
