Aberdeen are "increasingly hopeful" that 7,500 fans may be allowed at games at Pittodrie by the end of September.
The Scottish Premiership clubs were briefed by national clinical director Jason Leitch on Wednesday, ahead of the scheduled 1 August start to the season.
And Aberdeen chairman Dave Cormack believes clubs may now only have "a few games behind closed doors - four home games takes us through September".
"That's our best estimate right now," he added in a series of tweets.
In a club statement about season ticket sales, Aberdeen said they are making preparations to hold matches at Pittodrie both behind closed doors and with a partial capacity of 7,500.
One metre social distancing would be in place and the seats would be given to season-ticket holders, of which Aberdeen currently have 6,700.
"With positive progress on the fight against Covid?19, there may now only be a few home games behind closed doors, and we could get back to playing in front of partial crowds earlier than anticipated," the statement added.
On Tuesday, Prof Leitch told BBC Scotland there was "pretty much no chance of crowds in August".