First Minister Nicola Sturgeon welcomed statements from both clubs urging supporters to stay at home during Sunday's Celtic Park derby.
But no final decision has been taken on the fate of the game with a judgement promised "over the course of the next few days".
Rangers came under major criticism from the government over their response to thousands of fans gathering to celebrate their title win on March 7, and ahead of their game against St Mirren 24 hours earlier.
Ibrox boss Steven Gerrard and skipper James Tavernier, and Celtic counterpart John Kennedy issued messages over the weekend pleading with supporters to abide by lockdown restrictions.
"I hope the clubs will continue that over the next few days," Sturgeon said during a 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 don't want to be in a position, I never want to be in a position, of standing here and 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."
Kennedy and captain Scott Brown were later among a Celtic contingent which attended a briefing by national clinical director Jason Leitch.
A club statement read: "The Scottish Government has already made clear to Celtic that it does not in any way associate the scenes last weekend with Celtic or our supporters.
"The club will continue to be clear in our messaging to our supporters of the importance of staying at home in line with guidance throughout the pandemic."
Brown added: "We know it has been so difficult for our fans not being part of matches, but they have done brilliantly throughout the pandemic. Our supporters have been great in sticking to the guidelines, even after we have won the league and another treble, so we just need more of the same."
Chief medical officer Gregor Smith stated it was too early to understand the full impact of the title celebrations.