Richard Masters said the Premier League have discussed the cancellation of the 19-20 season for the first time during talks on Monday.
The Premier League suspended play on March 13.
"I'm happy to reveal it [curtailment of season] was discussed for the first time, but the contents of that discussion have to remain confidential," Masters told the media after Monday's four-hour video conference.
"It's still our aim to finish the season obviously, but it's important to discuss all the options with our clubs. What I can say is that all of the talk was about finishing the season. No conclusions were reached on any other models.
"Those are future conversations we may need to have. There was a desire to see all the different implications, the adaptations, if you like, to the Premier League model as we know in order to play out the season and then discuss what the fairest way forward is."