"If Annus does not give a sample by noon then it will be a breach and so he can say goodbye to his gold," Pal Schmitt told the Hungarian radio station.
Annus did not test positive at the Games and returned home, apparently against regulations, after winning the hammer on Sunday and announced his retirement.
The 31-year-old shares a coach with Hungary's discus gold medallist Robert Fazekas, who was expelled from the Games after refusing to provide a complete urine sample after Monday's final. Fazekas had to return his medal.
The International Olympic Committee (IOC) said earlier on Friday that they had asked Hungarian officials to find Annus so they could test him for drugs.
"Annus will be the subject of out-of-competition testing," IOC president Jacques Rogge told reporters on Friday.
"The IOC has asked the (Hungarian) NOC to notify the whereabouts of the athlete. We want to hear about this."
Annus said he had not taken any banned substances.
"My only sin is that I won the Olympic gold," he was quoted as saying by a Hungarian internet portal site.
Schmitt also said that the Hungarian Olympic officials had been contacted about a weightlifter, but said he had no further details.
