Cornell's death comes just a few days after the death of one of Pitt's other friends, former Paramount Pictures chairman and CEO Brad Grey.
WATCH: Chris Cornell Covered Led Zeppelin's 'In My Time of Dying' During Final Performance Before Death
"He is trying to process the loss of two great friends," the source said. "This has hit him very hard."
Pitt and Cornell's friendship goes back quite a ways, and so does the 53-year-old actor's admiration for the late rocker. In a 2004 interview, Pitt reportedly told Cinema Confidential, "I'm a big Chris Cornell addict, anything he does."
A few months after his split from Angelina Jolie, Pitt made one of his first public appearances to introduce Cornell at the ROCK4EB! charity event in Malibu, California, alongside Sting. "I get to introduce a very, very good friend of mine," Pitt said of Cornell before he and Sting performed The Police's 1983 hit, "Every Breath You Take," as well as Soundgarden's 1994 hit, "Black Hole Sun.Read more at Entertainment Tonight