Asger Leth is directing the picture starring Sam Worthington as a fugitive former police officer who threatens to jump off a ledge.
Elizabeth Banks is playing a hostage negotiator who has a relationship with the cop and tries to talk him out of jumping.
Burns and Rodriguez are also joining Jamie Bell and Anthony Mackie in the film, according to The Hollywood Reporter.
Burns will play a negotiator who attempts to take over Banks's role. Rodriguez is to portray a friend of Bell who tries to help Worthington's character prove his innocence.