This week, Deputy Prime Minister, Nick Clegg, announced that pupils in England would get free dinners.
Education is devolved to the Scottish Parliament and local councils run education departments so the announcement does not apply to Scots.
However, the cost of the policy is estimated by the UK Government to be £600million and funding rules mean Scotland will receive a share of around £60m added to its budget to spend as it likes.
Gordon Matheson, leader of Glasgow City Council, said the city should receive around £7m of that cash and wants to use it to provide free school meals for P1 to P3 pupils.
Earlier this month the Evening Times reported how Mr Matheson's Executive Member for Education Stephen Curran, rejected a call from SNP councillor, Norman Macleod, to provide free school meals.
He stated it would be too costly and other services would have to be cut. Now there is a likelihood of money being available from Westminster, the council wants to extend free school meals.
Mr Matheson said: "Glasgow City Council has already shown its commitment to young people by providing free breakfasts and free lunches for thousands of children in our schools.
"The UK Government's decision to extend free school meals to all pupils in P1-3 will require significant additional investment.
"We expect Glasgow to get more than £7m as our fair share of the extra money coming to Scotland to implement this policy."
The Scottish Government said it was committed to expanding free school meals to more pupils and would be waiting to see how much cash came from the UK government.
A spokesman said: "Nearly a quarter of primary school pupils are currently registered for free school meals in Scotland and school meal uptake continues to rise.
"We are committed to expanding this provision further and, once we see the financial implications of this announcement for Scotland, we will examine how best to deliver that expansion."
Mr Clegg announced the move for England in his party's UK Conference in Glasgow this week.