Levine, who has been the No. 2 man to Jon Daniels the last nine seasons, spoke with Arizona's chief baseball officer Tony La Russa about his desire to remain in Texas.
The Diamondbacks, who have a 66-88 mark entering Tuesday's play, are trying to replace Kevin Towers, who was fired Sept. 5.
According to CBS Sports'Jon Heyman, former big league pitcher and current agent, Dave Stewart will interview for the job soon. Stewart was also an assistant GM with the Toronto Blue Jays.
St. Louis Cardinals executive Gary LaRocque, Los Angeles Dodgers assistant GM DeJon Watson, Boston Red Sox executive Allard Baird, New York Yankees assistant GM Billy Eppler among others are under consideration for the Arizona job.