Labour MSP Michael McMahon is to ask the Scottish Government its position on the policing of a protest by fans' group the Green Brigade.
Glasgow councillors have also criticised the police's response to the pro- cession by the group, just before a Parkhead game.
Brian McConnachie QC said the 'kettling' of the group by around 200 officers was "overkill".
Last night, a spokesman for Celtic said the club was "very concer-ned" after seeing images from the incident and "claims by supporters of harassment and heavy-handed policing".
The club, which is to write to the chief constable on the matter, also provided e-mail addresses for fans with grievances to contact Celtic.
The 13 held have subsequently been released, eight to appear in court later and five who are subject to reports to the procurator fiscal.
The charges include breach of the peace, misuse of drugs, resisting arrest and assaulting a police officer.
On the "inaccurate" claim of heavy-handedness, a force spokeswoman said: "Senior officers are entirely satisfied the officers on the ground dealt with the situation in a professional and proportionate way."
Labour councillor George Ryan has written to Alex Salmond over the policing of fans, saying: "Police have reacted in a way that you, as First Minister, have called for since the introduction of the Offensive Behaviour at Football Act."
And Mr McMahon added: "None of this is addressing the problem of sectarianism", adding that a backlash was driving a wedge between supporters, the police and clubs.