Clooney will direct and star in the new World War II period drama and wants Damon for a role.
Damon looks set to join an all-star cast including Daniel Craig, Bill Murray, Cate Blanchett, Jean Dujardin, John Goodman, Hugh Bonneville and Bob Balaban, reported Aceshowbiz.
The script was adapted by Clooney and Grant Heslov from Robert M Edsel's true-life book of the same name and recounts the final chapter of Hitler's rule as the Nazis begin to realise their fight is hopeless.
Filming will begin in an undisclosed European location in January.