According to The Wrap, Drake, whose real name is Aubrey Drake Graham, is currently in negotiations for an unknown role in the film.
Arbitrage follows a hedge fund magnate who desperately tries to avoid being arrested for his fraudulent activities.
Susan Sarandon and Eva Green have already been cast in the movie, which is being written and directed by The Informers helmer Nicholas Jarecki.
Arbitrage would mark Drake's second film appearance following a supporting role in the 2007 comedy Charlie Bartlett.
Drake rose to fame as a long-running cast member on teen drama Degrassi: The Next Generation, after which he released his debut album last year.
Production on Arbitrage is scheduled to begin in March.