Coleman told the Daily Caller that if current chairman Michele Steele runs again, Coleman will not challenge him.
"If he's in, then I'm out," Coleman said.
Steele, who has been criticized recently for his performance by numerous prominent Republicans, including his former political director Gentry Collins and Gov. Tim Pawlenty, has not publicly said whether he will seek another term at the helm of the RNC.
Coleman, currently CEO of the right-leaning American Action Network, did leave himself a window open for the top RNC job, declining to state what he'd do should Steele elect not to run.
"I'm not in a position to speculate what-if-he-doesn't," Coleman said. "At that point, it becomes speculation."
