The American Olympic and world 100 metres champion was banned for up to eight years on Tuesday after agreeing that his positive drugs test constituted a doping violation.
Gatlin also agreed to help fight drug abuse in the sport, and the actual length of his suspension will be decided by an arbitration panel.
"Four years would be the minimum," IAAF spokesman Nick Davies told the BBC. "We want to see if it leads to other convictions.
"We want him to tell the truth about what really happened. If Gatlin just says 'I don't know what happened,' that's not good enough."
The 24-year-old Gatlin, who has lost his share of the 100 metres world record, tested positive for the male sex hormone testosterone at the Kansas Relays in April for reasons he said he did not know.
It was his second positive test, which under anti-doping rules could have resulted in a life ban.
