A total of 15 clubs - which is understood to include several top flight teams - told the Conservatives they support a trial, while two of the clubs who responded said they oppose the idea.
Tory leader Ruth Davidson said 88% of the clubs that had responded to their survey are "clearly in favour of a pilot project" to see if the existing ban on drinking at matches could be lifted.
First Minister Alex Salmond told MSPs at Holyrood that Police Scotland are currently "not minded" for the ban to be relaxed.
He added that drink was a "major contribution to disorder in society and to disorder and offensive behaviour at football matches".
But Ms Davidson said: "Supervised, responsible drinking happens in other sports in Scotland and with football in other countries. Are we really saying that Scottish football fans cannot be trusted?
"I've written to every senior club in Scotland to canvass opinion, as well as to the Chief Constable of Police Scotland to discuss any security concerns.
"Of the clubs that responded to our survey, 88% were clearly in favour of a pilot project to see if the ban can be lifted."
She added that having "properly supervised alcohol" on sale inside football grounds "could be an important new revenue stream for Scottish clubs".
Ms Davidson argued: "All-seater grounds and extra measures address some of the safety fears of the past, when this ban was brought in.
"Why not try a pilot project to see if what we know works well elsewhere can work here too? The fans want it, the clubs want it and it is in everybody's interest to make any relaxation of the rules work."
She was speaking after SNP backbencher Jim Eadie said a survey of supporters had found 62% want the ban lifted.
"Scotland has moved on significantly since the alcohol ban was imposed almost 30 years ago, with all seater stadiums," he said.
"Isn't it time then that we reviewed the ban and would it not be possible to lift it on a trial basis?"
Mr Salmond said decisions on this were "informed by Police Scotland, who confirm that they at this stage are not minded to seek a relaxation of the controls on alcohol at football matches, but are engaging with interested parties on this matter".
The First Minister said his Government is "committed to working with all parties to improve the match day experience and also ensure that football fans enjoy our national sport in a safe, enjoyable environment".
But he said: "We have to have an approach which understands alcohol is a major contribution to disorder in society and to disorder and offensive behaviour at football matches."