Celtic hope to have close to 25,000 supporters in attendance for their first Scottish Premiership home match against Dundee on 7 August.
The Glasgow club have received permission for 18,500 fans to watch Saturday's friendly with West Ham.
A crowd of 9,000 watched Tuesday's 1-1 draw with Midtjylland.
Following talks with the city council, Celtic say they are "encouraged by the indicative figure of around 24,500 for the subsequent home game".
Premiership champions Rangers have already been given the go ahead for 17,000 fans at their opener with Livingston on 31 July.
A Celtic statement read: "We can assure our supporters we will be doing all we can to work closely with the relevant authorities and welcome our fans back in even greater numbers in the coming weeks.
"We want nothing more than to welcome as many fans back to the stadium as quickly as possible and therefore appreciate your patience as we continue to work behind the scenes to make that happen."
Restrictions eased on Monday, with Scotland moving to level zero in the fight against Covid.
Seated crowds of 2,000 will be able to attend matches, while applications for more can be made on a case-by-case basis.
Aberdeen will welcome 5,655 fans to Pittodrie on Thursday and Hibs will have 4,700 inside Easter Road at the same time as both clubs enter the Europa Conference League.
National clinical director Professor Jason Leitch has indicated that stadiums in Scotland could return to full capacity on 10 August.