The Argo actor will join Sylvester Stallone, Robert De Niro, Kevin Hart and Kim Basinger if he signs up for the project.
Get Smart helmer Peter Segal will direct the movie based on a screenplay by Entourage writer Doug Ellin. Bill Gerber, Carrie Gillogly and Mark Steven Johnson will act as producers.
Grudge Match is based around a rivalry between two ageing boxers, played by Stallone and De Niro, who plan one final match against each other.
Basinger has been cast as the female lead caught up in the rivalry, while Arkin is in discussions to play the trainer to Stallone's character, Variety reports.
Grudge Match is yet to receive a release date.
Watch a trailer for Argo below: