The Avengers actor was keen for Murray to appear in the Marvel Studios movie, but was unable to get in contact with him.
"Downey told me, 'We wanted Bill to consider a role in Iron Man, but nobody could find him'," interviewer Scott Rabb told Murray in Esquire.
"Show people are awestruck by your inaccessibility."
Murray responded: "I'm not trying to be coy. It's just practical for me. When the phone started ringing too many times, I had to take it back to what I can handle.
"I take my chances on a job or a person as opposed to a situation. I don't like to have a situation placed over my head."
The Moonrise Kingdom star is known for not having an agent and simply directing interested parties to a seldom-checked voicemail.
It is not known which Iron Man film or role Murray was wanted for.