The Scottish Government are weighing up the options regarding the derby clash on Sunday, March 21.
It follows the scenes which greeted Rangers’ Scottish Premiership title win at the weekend.
Thousands of supporters took to the streets around Glasgow to celebrate, breaking Covid-19 regulations.
BBC Sportsound host Kenny McIntyre said: "Our news colleagues are reporting that the Scottish Government are looking at various options ahead of the Old Firm match, one of which is cancelling it."
The celebrations provoked a degree of angst between Rangers and the Scottish Government with First Minister Nicola Sturgeon taking to Twitter to ask for the club to tell fans to go home on Sunday.
Sturgeon revealed a decision on the match will be taken in “due course”.
She said: "In terms of future fixtures, there are a variety of discussions happening over the course of this week including one between myself and the chief constable later today.
"We will report back on those in due course certainly before the scheduled Old Firm match on March 21.
"The reason we've tried to keep football and elite sport generally going is not for the benefit really of the elite sports people but for the fans.
"Everybody is being deprived of so much right now that the ability to watch a football match and cheer on your team on the television should be something that people have the ability to do.
"So I hope that we don't have to spoil that for the majority but we will have to assure ourselves that there will be no repeat of the kind of scenes we saw at the weekend.”
Rangers chairman Douglas Park sought to defend the club against “claims” made by the Scottish Government.
A letter to Sturgeon said: “I must reiterate my concern and displeasure at the claims of the deputy First Minister that there is a lack of leadership at Rangers Football club.
"I think this is particularly disingenuous given the fact we have outlined the timeline above and more importantly the fact you have failed as a constituency MSP to engage with us directly on this matter.
"That to me is a lack of leadership and a dereliction of duty.”