Reports at the weekend said Clydesdale Bank Premier League clubs could be asked to pay extra cash for policing at matches or pay for their own private security.
Sir John Orr, honorary president of the Football Safety Officers Association in Scotland, has called for further discussions before any changes to the policing of football grounds are implemented.
Orr - the former chief constable of Strathclyde Police - said: "It would be helpful if any change to the current format is the subject of wide and appropriate debate."
Top flight clubs Celtic, Rangers, Kilmarnock, Hamilton, Motherwell and St Mirren come under the jurisdiction of Strathclyde Police, whose chief constable Stephen House is expected to announce the new plans to members of the Strathclyde Police Authority this week.
Speaking in the Sunday Mail, he said: "We have recommended overall responsibility for safety is transferred to its rightful owner - the management of the stadium."
Responding to the comments, Orr said: "The safety of everyone at football matches is paramount and the association welcomes any discussion regarding the levels of police and stewarding resources within such grounds.
"The debate surrounding the charging of football clubs for the deployment of police officers outside stadia has, over the years, been regularly discussed by relevant authorities.
"In my view this is an extremely difficult area to reach measured and just conclusions as police officers face multiple challenges in the performance of their duty but are, by statute, required to prevent crime, maintain law and order and protect persons and property wherever the locus and the circumstances of that requirement may be.
"Police officers routinely and effectively police demonstrations, marches, parades, open air gala days, concerts etc without seeking payment of territorial policing costs from the organisers.
"To charge for any geographical `footprint` which is believed to emanate from a football match it would be fundamentally necessary to show that the policing presence involved, in all balanced and objective fairness, was directly and necessarily related to the match taking place."