Smith had been asked to take over the Premier League club on a short-term 13-game contract as they look to secure their top-flight status.
However, Wolves will have to look elsewhere if they are to bring in a new manager after the 63-year-old rejected the chance to return to management.
"It's true I'm not going [to Wolves]," he told the Express and Star.
"I was totally unsure whether I really wanted to do it or not. It was a purely personal thing, nothing to do with Wolves.
"I know [chief executive] Jez Moxey and knew I was more of a fall-back than anything. We didn't even get as far as discussing money.
"There was never a face-to-face meeting and we never discussed finance. If someone asks you, you're pleased to be asked, but the longer you think about it, you start to ask yourself whether it was right."
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