The X-Men: First Class star could head to London in July to film the project, reports Deadline.
Eran Creevy is the writer-director behind the movie, which is described as "an epic crime thriller in the mould of Heat or Internal Affairs".
The actor recently joined the cast of Robert Redford's upcoming film project The Conspirator, also starring Robin Wright.
McAvoy recently said that the dynamic between Charles Xavier and Erik Lehnsherr in X-Men: First Class makes the film "kind of a love story".
View the trailer for X-Men: First Class, featuring James McAvoy, below: