Variety.com said Sarah Jessica Parker also is in negotiations to co-star with Grant in the untitled movie about an estranged New York couple who witness a slaying and are whisked away together in the federal witness-protection program to a small town in Wyoming.
Lawrence also wrote the movie.
Grant is best known for his roles in "Four Weddings and a Funeral," "Bridget Jones' Diary" and "Love Actually."
Parker was recently seen in "Sex and the City," the big-screen follow-up to her former HBO comedy series of the same name.
Lawrence also wrote the "Miss Congeniality" movies before he made his directorial debut with "Notice."