Warner Bros have been courting Nicholson to star in the David Dobkin-directed movie, according to The Hollywood Reporter.
Nicholson has reportedly received an unofficial offer to appear in The Judge, which casts Downey Jr as a successful attorney who returns to his hometown for his mother's funeral.
When he discovers that his estranged father - the town's judge, who has Alzheimer's - is the chief murder suspect, he sets out to find the truth in a journey that sees him reconnecting with his roots.
Nicholson has only appeared in three movies since 2003. It reportedly took Leonardo DiCaprio and Martin Scorsese to convince him to appear in Warners' 2006 movie The Departed after he rejected the role of Frank Costello several times.
Downey Jr and Nicholson are reported to be meeting later in the week to discuss The Judge, which is expected to be the former's first film of 2013.