No, we're not talking about the current Bond search, we're talking about the early 70s. Sean Connery wanted more money and didn't really want to continue in the role, so the producers offered it to Reynolds, who turned it down because "an American can't play James Bond." He still regrets it.
Oddly enough, an American actually was the first person to play James Bond. Barry Nelson played 007 in a 1950s episode of the TV series Climax! Nelson, an American, was the first person to play Bond on film.