The Limitless star appeared to openly insult Crowe during a recent interview, but did not elaborate on his problem with the Gladiator star.
"Russell Crowe. S**t. He is. Next level," Cooper told Esquire recently.
While the two have never worked on camera together, Cooper's ex-girlfriend Renée Zellweger starred opposite Crowe in the 2006 drama Cinderella Man.
The actor also said that he tries not to think about the celebrity gossip side to being an actor, and admitted that it can often be detrimental to your career to be associated with that side of things.
"Being in Us Weekly does not make you famous," Cooper explained. "Paul Thomas Anderson does not read US Weekly and go, 'Hey, look at this guy! I want this douchebag in my next film.'"
Since splitting from Zellweger in March earlier this year, Cooper has been linked to Tron Legacy star Olivia Wilde.
Cooper's latest film, The Hangover Part II, is released in cinemas this weekend.
Watch the trailer for The Hangover Part II below: