Jenny Sanford had run Sanford's successful congressional campaign in 1994.
"Since you're not running, I want to know if you'll run my campaign," Sanford said, according to the magazine. "We could put the team back together."
The former governor's wife declined.
Sanford previously told The Hill that he checked with Jenny Sanford before deciding to run. He said that it would be a mistake for both himself and his ex-wife to get into the race.
“I went out to the beach house on Sullivan’s Island; we visited on the front porch,” Sanford said.
“I told her if she had an interest in doing this, that I’m out, because there’d be nothing crazier than a husband and a wife running against each other. It'd be a circus."
Sanford and his wife divorced after news surfaced that he had had been having an affair with an Argentine woman in 2009. In January, the former South Carolina governor announced that he would run for for now-Sen. Tim ScottTim ScottOvernight Finance: Trump's Labor pick withdraws | Ryan tries to save tax plan | Trump pushes tax reform with retailers Puzder withdraws nomination for Labor secretary Ryan tries to save tax plan MORE's (R) congressional seat.
In his first campaign ad in the special election, Sanford addressed the affair.
"For years, while many have talked, I’ve fought to do something about it. I’ve cut spending, reduced debt and made government more accountable," Sanford says in the ad. "More recently, I’ve experienced how none of us goes through life without mistakes, but in their wake we can learn a lot about grace, a God of second chances and be the better for it."