Count Secretary of State Jesse White and Ald. Walter Burnett (27th) out.

Neither prominent politician will be running for mayor.

White is in his fifth term and is seeking reelection.

His spokesman said the mayorship is one of the four jobs White would never want.

Burnett said he was “flattered” and “honored” when his name started circulating as a potential successor to Mayor Rahm Emanuel, who earlier this week announced that he wouldn’t be running for a third term.

But Burnett didn’t feel “called” to run for the job “this time.”

“There’s a lot more I need to do in my ward and I love my job,” Burnett said. “I’ve got a hot ward and there’s a lot to do to continue to grow. I made commitments and I have to try to keep them.”

“I think I can do better for my ward and for the city if I’m on the sidelines trying to help.”

While Burnett said he could probably keep his promises if elected mayor, he said whoever fills Emanuel’s shoes will face a lot of challenges.

Burnett’s not ruling out a run in the future, though. After the shakeup, he says he may be fourth or fifth in seniority and “young enough to be around long enough to move up” in the future.