Stojkovic, who spent eight years with the J-League club, has emerged as the leading contender to take over from Dutchman Sef Vergoossen, who has signalled his intention to quit at the end of the 2007 season.
"He is one of the candidates we have approached," Nagoya spokesman Yoshihiro Fukushima said of Stojkovic, who resigned as president of Serbia's Red Star Belgrade last week. "He has strong links to Grampus Eight and has us in his plans."