According to Variety, Arkin is in negotiations to join Affleck's next directorial project as an ex-CIA agent called Lester Seigel.
The film follows a secret CIA mission to rescue six diplomats being held hostage in Iran in 1979, by convincing the authorities that they were there filming a science fiction film.
If cast, Arkin will play a Hollywood producer who used to be an agent himself, who is drafted in to assist on the mission.
Arkin is best known for his Academy Award-winning role in Little Miss Sunshine and will next be seen opposite Ryan Reynolds in The Change-Up.
Affleck had been linked to a role in Baz Luhrmann's upcoming adaptation of The Great Gatsby, but is said to have dropped out in order to focus fully on Argo.