Damon, who will take on Campbell's role as Texas Ranger La Boeuf in the Coen brothers' remake, admitted that he doesn't plan to use the role to launch a singing career.
"No singing, you'll all be spared!" he said at the UK press conference for Green Zone.
Country singer Campbell was hand-picked by John Wayne to star in the 1969 Western and his song 'True Grit' went on to secure an Oscar nomination. The remake will feature Damon, Josh Brolin and Jeff Bridges in the lead roles.
Damon added that the Coens will go "right back to the source for True Grit".
"It's a wonderful book that Charles Portis wrote, most of the dialogue is culled right from the book. I'm relying less on Glen Campbell and more on Joel and Ethan Coen for that performance," he said.