Clooney directs and also stars as a Democratic governor running in the presidential primaries.
Ryan Gosling, Marisa Tomei, Evan Rachel Wood, Paul Giamatti and Philip Seymour Hoffman also star in the film.
No release date has been set for the film, but officials said Clooney's Smokehouse Pictures plans to open a production office in the area.
Clooney's father, Nick, has worked as a TV news anchor in Cincinnati and also wrote a newspaper column there.
The Associated Press contributed to this report.