"I thought about it but I haven't resigned. If I do, I will officially notify the FSSCG executive board, rather than do it over the telephone," the daily quoted Stojkovic as saying.
Daily Politika, Serbia's leading newspaper,
reported on Saturday that Stojkovic and national team coach Ilija Petkovic had resigned.
It quoted Stojkovic as saying he was "no longer capable of taking the country's soccer back to winning ways" and that "it was time for others to take over".
Stojkovic and Petkovic had decided to step down after a string of poor results culminating in failure to qualify for either the 2002 World Cup or Euro 2004, it said.
Neither of the men were immediately available for comment but Blic quoted Stojkovic as saying he would announce "radical changes" within the FSSCG at a news conference next week.
"There will be cuts, that's all I can say at the moment," he said.
Many football fans called for both Stojkovic and Petkovic to quit after a long and miserable spell was compounded by the Olympic team's poor showing at the Athens Games, where they lost 6-0 to Argentina, 5-1 to Australia and 3-2 to Tunisia.