Fans gathered in George Square and at Ibrox on 7 March when Rangers were confirmed as champions
Rangers and Celtic need to show “strong leadership” in urging fans to stay away from Sunday’s derby, says the chairman of the Scottish Police Federation.
The Scottish government has yet to decide if the game at Celtic Park will go ahead as scheduled.
There are concerns after thousands broke Covid guidelines to celebrate Rangers’ recent title success.
“It’s not just about one statement or one day’s worth of social media,” David Hamilton told BBC Sportsound.
“It needs to be consistent and persistent.
“People who are putting the match at risk need to be treated by the clubs from a disciplinary aspect, with (the promise of) bans and so on.
“We need to see strong leadership from the clubs,” added Mr Hamilton. “So far we’ve seen a few videos but it needs to be continuing and there needs to be some kind of understanding about what the consequences of this are. Not just on an individual basis but in terms of what this could mean for the game.”
First Minister Nicola Sturgeon has welcomed statements from both clubs asking supporters not to gather.
“I hope the clubs will continue that over the next few days,” Sturgeon said during Monday’s coronavirus media briefing.
“It’s not just one statement and the work is done. As we know from experience of the last year, these communications are really important on an ongoing basis.
“I spoke to the chief constable personally last week about his views on what might transpire if the Old Firm match goes ahead. The justice secretary (Humza Yousaf) has been in contact with police and we will be in further contact with police over the course of this week.
“They will have intelligence of their own on whether it appears to them that fans in the main are following the advice or whether there is a significant risk of fans coming out to gather. On the basis of all of that we will have to take a judgement.
“I never want to be in a position, of saying football matches can’t go ahead, or any of the other things that we really enjoy in life can’t go ahead.
“But that’s the reality while we are still in this position. Big gatherings present a risk of transmission and we are trying to get transmission as low as possible so that we can open up all of the things we enjoy doing.
“That’s why we have to be careful and considered about this. I think a lot of people felt aggrieved at what happened a week past Saturday and Sunday, and understandably so because everybody is still living under these difficult restrictions.”