Celtic have called on the Scottish Government to allow fans into matches.
Peter Lawwell, the club's chief executive, wants to see a "phased return" of supporters at games.
The new Scottish Premiership season is due to kick off behind closed doors on 1 August.
Lawwell says he has discussed with the government the idea of Celtic hosting "pilot" games which would be watched by a set number of supporters.
The Celtic chief is anxious Scotland is not trailing when sport in the rest of the UK starts to open its doors to spectators.
Spectators will return at selected sporting events in England later this month, with a view to crowds coming back more widely on a socially-distanced basis from October.
The World Snooker Championship, the Glorious Goodwood horse racing festival and two county cricket friendlies will pilot the return of spectators, who have been unable to attend sporting events since the suspension of mass gatherings in March due to the coronavirus pandemic.
The news was announced as part of a further easing of lockdown measures by Prime Minister Boris Johnson on Friday, which in some areas appear to put him at odds with his chief medical advisers.
Nevertheless, the 'stage five' guidance on the return of spectators to English venues has now been issued, with October 1 the target date if the trials are successful and should conditions in the country at that time allow it.
Lawwell believes Scotland should follow suit. He said: "We have discussed the idea of 'pilot' games with the Scottish Government and believe it provides a safe, sensible way forward. As a club, we have put enormous thought and effort into making Celtic Park fully compliant with all public health-related requirements while allowing our supporters to return to watching football.
"It is acknowledged that Scottish football has been exemplary in implementing all the safeguards required of it, first to get back into training and, from August 1, to playing competitive SPFL matches.
"We are convinced that this should now be accompanied by a phased return of spectators which would be good, not only for the game of football but also for public health and morale in Scotland more generally.
"Scottish clubs are much more dependent on matchday revenues than other, larger leagues. That factor should be taken account of, so long as the public health obligations are met, to which we are entirely committed.
"We also have an obligation to our own supporters to make the case for them to be allowed to watch live football, particularly when they can see the steady progress towards this in other European leagues.
"Alongside other sporting bodies, Celtic will continue to engage in constructive dialogue with the Scottish Government and look forward to early progress."
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