Greek deputy sports minister Lefteris Avgenakis has said the country's top football division might be able to restart, as players prepared to return to training.
Greece is slowly lifting restrictions after a near two-month lockdown due to the coronavirus pandemic.
Avgenakis said the restart "will be done step by step".
"The complete lifting of the restrictive measures cannot be answered today. We respect the advice of health experts and our first priority is human life," he said, adding if the Super League is allowed to resume, it would be behind closed doors.
The 14 top-flight clubs will on Tuesday start outdoor training sessions of six to eight players, following strict hygiene and social distancing rules.
It has not been announced when the postponed league play-offs will take place, with officials hoping the campaign can start by June 14, pending permission from the government.
"We are sure that no one will risk the health of the athletes," Avgenakis said.