Hinch is currently serving a one-year suspension for his role in the Astros' sign-stealing scandal so must wait to interview with the White Sox until after the World Series concludes, according to Heyman.
The 46-year-old posted a 481-329 record over his five seasons in Houston. Under his guidance, the Astros reached the playoffs four times, won 100 games in three straight years, and earned two pennants and a World Series title. Despite that success, he was fired in January shortly after the league suspended him.
Another candidate to take over for the fired Rick Renteria is Hall of Fame skipper Tony La Russa, who last managed with the St. Louis Cardinals in 2011.
La Russa, who started his managerial career with the White Sox in 1979, was reportedly given permission to interview in Chicago by the Los Angeles Angels, with whom he currently works as a special assistant. He's close friends with White Sox owner Jerry Reinsdorf, who Heyman adds is keen on bringing the 76-year-old back to the South Side more than 30 years after firing him.