Both clubs issued messages to fans urging them to stay at home if the match takes place, following criticism of Rangers response to their supporters' title celebrations.
Speaking at the Scottish Government media briefing, First Minister Nicola Sturgeon welcomed the clubs' statements but added that a final decision on whether the game would go ahead had not yet been taken.
"I hope the clubs will continue that over the next few days," she added. "It's not just a one statement and the work is done.
"I spoke to the chief constable personally last week on his views on what might transpire if the Old Firm match goes ahead. We will be in further contact with police over the course of this week."
The match is due to take place at Celtic Park on Sunday with a 12 noon kick-off.