Aberdeen are "hopeful" of having 5,655 fans at Pittodrie for their Europa Conference League qualifier against BK Hacken next Thursday.
The club initially applied for permission to host just over 8,000 fans for their opening games of the season.
But they say due to 1m social distancing rules remaining at Level 0 that is no longer possible.
The club added it believes council officials are "satisfied" they can safely host just over 5,000.
"This positive feedback of our highly regulated environment combined with government and scientific advice that controlled outdoor events are more acceptable than indoor gatherings gives us confidence that we will get the go?ahead from the local authority," said chairman Dave Cormack.
Clubs in Scotland will be allowed to host 2,000 fans without prior permission from Monday 19 July, but can request greater numbers from their local council on a case-by-case basis.
Celtic have already asked if they can have 18,000 fans at Celtic Park for their Champions League qualifier against Midtjylland on Tuesday.