The redheaded actor has been rumoured to be in the running for the role for years, with bookmakers William Hill slashing the odds on him taking the part from 25/1 to 3/1 back in 2015.
But Damian told Britain's Daily Telegraph newspaper that while Bond is one of the most sought-after roles in the industry, he has no interest in becoming the next 007.
"I don't want to play Bond. I'm ambitious for different things. I don't know who they'll choose - he'll be fantastic or she will be fantastic. But I don't want to play Bond - even if I was asked!" he told the newspaper.
Damian's remarks come after Bond boss Barbara Broccoli insisted they won't reveal the next actor to take on the super spy role until after Craig's last outing as 007, "No Time to Die", hits cinemas next year (21).
"I always say, 'You can only be in love with one person at a time,' " she told Total Film. "Once the film's come out, then some time will pass, and then we'll have to get on to the business of the future. But for now, we just cannot think about anything beyond Daniel."
Rumor has it, Tom Hardy and Harry Styles are among the frontrunners seriously considered to be the next 007 superspy agent. "Don't f**k it up," Daniel Craig recently warned his successor. "It's a beautiful, amazing thing. Don't f**k it up! Leave it better than when you found it."