Officers say they will monitor the situation
The warning was issued by the Association of Scottish Police Superintendents (ASPS), which says it will keep a close eye on any trouble over the course of the campaign.
Last season, football games being screened live on satellite television were played on a Sunday evening.
But ASPS president, Chief Superintendent Allan Shanks, said the move could lead to an increase in city centre violence.
And the organisation said it would be considering whether to call for a change in the way football matches are licensed to give local councils a say in when games are played.
"Saturday evenings are already busy and we think that having games on Saturday night could have implications on the police and the community," he said.
"Supporters will have longer to consume alcohol before the kick-off and when they come out of the ground at about 1930 there is the potential for them to frequent already busy pubs and clubs.
"The majority of football fans are well-behaved, but we are going to monitor the situation over the coming season to see what the impact is.
"We are only speculating that there is the potential for an increase in disorder, but if our fears are realised then we will want to raise the issue with the Scottish Executive to see if the legislation can be changed.
"At the end of the day, we don't want to be killjoys because a lot of people
enjoy going to football games, but we are just concerned that perhaps the
commercial interests have taken precedence here."
The Bank of Scotland Scottish Premier League said it had extremely good relations with police throughout the country.
"We liaise closely with them on matters of safety and security," said a spokesman.
"Indeed, at many games SPL staff are situated within the police control centres to ensure that proceedings run smoothly.
"We have an ongoing dialogue with the police authorities and should there be any contact from the ASPS it will be dealt with in the appropriate way."