Renfrewshire Council leader Mark Macmillan said the proposal, made by the opposition SNP group, was too risky at a time when the Labour-run authority faced a "dire lack of public finances".
He was responding to a call from SNP group leader Brian Lawson urging the council to look at becoming involved with the club, which has a 52% share holding for sale at an estimated £1.5million.
Councillor Macmillan said "I can understand and appreciate the merits of true fan ownership of a football club.
"But in the present circumstances, with the dire lack of public finances to run vital services for the people in our communities and the swingeing cutbacks from the Tory/Lib-Dem Coalition being passed on to local authorities by the SNP Government in Holyrood, it would be irresponsible for us as custodians of the public purse to spend taxpayers' money on buying a football club.
"We also have to consider what Councillor Lawson wants us to buy into.
"He is suggesting we use the hard-earned money of the people we represent to buy a football club at a time when Scottish Football is in a perilous state over the crisis at Rangers FC."
And he added: "We are restoring the school buses that councillor Lawson axed. We are removing the charges imposed by councillor Lawson on some of the most vulnerable members of our community to travel to adult day services.
"Councillor Lawson has been extremely vocal in challenging our decision to do this by asking where the money is coming from and what services are going to be cut to do this.
"I would now ask Councillor Lawson to tell the people of Renfrewshire where he thinks the money is coming from and what services does he propose to cut to spend Renfrewshire taxpayer's money buying a football club."
Outlining his motion, being debated by the council today, councillor Lawson said: "I have no wish for a council committee to pick the team, but the council should at least investigate how it can play a bigger part in the club.
"This might be as little as assisting in finding external funding to purchase all or part of the shares which are up for sale or even the council itself taking a share in the club.
"I am very aware of the council's tight budget position, but we have to at least investigate if and how we can work more closely with St Mirren.
"It would be a shame if it was taken over by rich foreign owners who were only interested in the value of the ground and the players."