Rangers has challenged the validity of a video which appears to show an anti-Catholic chant at an event with players at Ibrox.
Police Scotland said it is examining social media footage which is claimed to show sectarian singing in a lounge at the stadium on Saturday.
Rangers said they were concerned that an "attempt to discredit players" had been "taken as genuine".
The club had just won their first Scottish Premiership title in a decade.
Justice Secretary Humza Yousaf told the BBC he was "disgusted" and said if the footage was genuine then those involved should be "booted out of the club".
Police Scotland said: "We are aware of a video circulating on social media apparently showing Rangers players using sectarian language while celebrating on Saturday.
"We are assessing its contents and will liaise with the Crown Office and Procurator Fiscal Service as part of our inquiries."
Assistant Chief Constable Gary Ritchie said: "We're looking at that now to see if we can identify any individuals who are committing offences."
He said they would "take action" if any offences were identified.
I have also been made aware of this clip, if (and I stress if) this clip is genuine then any player or staff member found to be guilty of anti-Catholic hatred should be shown the door by the Club.— Humza Yousaf (@HumzaYousaf) May 17, 2021
It is right Police Scot investigate & determine the facts around it. https://t.co/wRyI5ZP4Tz
Rangers said it was "deeply concerning" that the video had been taken as genuine, and highlighted the dangers of "trial by social media".
A statement from the club said: "It is evident that this video was shared with an adjoining narrative which attempts to discredit our players and the reputation of Rangers Football Club.
"We are confident that no criminality took place, we have sought legal advice and look forward to cooperating with Police Scotland."
The club added: "Sectarianism is unacceptable and has no place in our club which is underlined by our Everyone Anyone campaign."
Humza Yousaf said it was right for Police Scotland to "determine the facts" around the video.
He told BBC Scotland: "Let's not call it sectarian, it's anti-Catholic.
"If that video is genuine, then first of all I'm pleased that Police Scotland are investigating and they will liaise with the Crown to see if any criminality has taken place.
"Any Rangers player or staff member who has engaged in that anti-Catholic hatred should be booted out of the club."
Rangers' win on Saturday was followed by disruption in Glasgow when thousands of fans took to the streets to celebrate.
They marched from Ibrox Stadium to George Square, where flares were set off and missiles thrown.
Police broke up the crowds after about five hours due to "rising disorder", with one officer suffering a serious facial injury.
Police Scotland has set up a dedicated team to investigate.
They hope to track those involved and are using an online portal for members of the public to upload video or photos of the incident. CCTV footage is also being analysed.
Det Insp Craig Warren, who is leading the investigation, said: "The public can be confident we are doing everything possible to identify those responsible for the violence and disorder on Saturday.
"This will take time due to the numbers involved. Rest assured, if you were involved in causing this disorder, violence or anti-social behaviour you will be arrested."