The retired general and the Arizona senator have both repeatedly said they don't want the number two spot in a Bush administration. And Bush, the Texas governor and GOP presidential candidate, is taking them at their word.
"People who don't want to be considered for vice president are not going to be considered for vice president," Bush told The Associated Press.
"They have told me, they have said publicly, they don't want to be vice president," he added.
Even so, Bush left the door open just in case, aware that Powell and McCain are popular with voters and would only boost the GOP ticket.
"If they ever change their mind, I'll let you know," he said.
Bush said he knows what Powell - the former chairman of the Joint Chiefs of Staff - would say if asked to be considered.
"The answer," said Bush, "is no."
Powell has not ruled out a Cabinet post and his name has been mooted for Secretary of State. McCain - Bush's GOP primary rival who has since endorsed the governor - has been bandied about as a possible Secretary of Defense.
Bush said "a couple dozen" prospects are on his short list for a running mate. The governor said he talks frequently about the choices with Dick Cheney, the former defense secretary in charge of his search. Each prospect undergoes an initial background review.
"I'm looking at everybody," said Bush. "I'm watching it (the process) very closely."
Pennsylvania Gov. Tom Ridge is said to be a top contender, but the swirl of speculation ranges from Michigan Gov. John Engler to former Cabinet secretary Elizabeth Dole.
Bush and Cheney are trying to determine the best time to announce his choice. The governor said he is considering an earlier-than-usual unveiling, noting that recent vice presidential candidates have been announced at or near the GOP convention.
Still, with the convention opening July 31 in Philadelphia, Bush said he could not imagine making his selection in May or June.