Greek Super League clubs voted on Wednesday to resume the season by 14 June if it receives permission from the government.
The post-season play-offs to determine who wins the title, as well as Champions League and Europa League spots, have been postponed due to the coronavirus pandemic.
A ban on sporting activities as part of a nationwide lockdown is currently in force.
Media reports said that the government may announce its decision on whether the league can continue as soon as Thursday.
"The league cannot start after 14 June," said league president Minas Lysandrou following a teleconference with the clubs' owners.
He said training should start by 25 May at the latest, with an ideal date of 18 May, and that matches should restart by 14 June.
Ten of the 14 teams in the talks were in favour of continuing the championship, including regular season leaders Olympiakos and third-placed AEK Athens.
PAOK Thessaloniki, Panathinaikos, Panetolikos and Panionios were against playing.
"If the championship starts we will lose much more than we will gain," said Panathinaikos boss Giannis Alafouzos.
PAOK sit second in the table, just one point ahead of AEK in the race for a place in Champions League qualifying.