The meeting was announced on Monday by transition team officials, the Washington Times reported.
Petraeus, a four-star general, also served as CIA director from 2011 to 2012 when he resigned after he admitted sharing classified information with his biographer, whom he had an extramarital affair with.
The other top candidates for the job are former Massachusetts Governor Mitt Romney and former New York Mayor Rudy Giuliani, who have been met with criticism.
Asked if the president-elect was nearing the end of his search for a secretary of state, a spokesman said,"He'll complete that when he's ready.
He's going to pick the person that he thinks will do the absolutely best job."