The SNP want the council to provide the meals this year and the council leader has asked the Government to give the money earlier to allow free meals from August this year.
The SNP estimated the cost of providing free school meals to all P1-P3 pupils would be just under £3m, council leader, Gordon Matheson, however has said Glasgow should get a £7m share of the £55m cash from Holyrood.
The council said there are extra costs associated with equipment, staffing and supervision of the greater number of children as well as food costs. Mr Matheson has written to John Swinney, Finance Secretary, seeking the £7m in time for when children return after the summer.
He said: "The purpose of this letter is to urge the Scottish Government to allocate to Glasgow a fair and proportionate share of the estimated £55m allocated to Scotland.
"This would allow us to provide free school meals to all pupils in P1 - P3 and would see an additional 6000 pupils in Glasgow each day taking a school meal.
"It is essential local authorities receive their proportionate share of this funding so that such a fundamentally important policy can be properly implemented in time for the start of the new school year in August 2014."
SNP councillor, Norman MacLeod, wrote to Mr Matheson requesting an earlier start.
He wrote: "Will you join with me in seeking ways in which we can introduce this policy in Glasgow from the beginning of the new school year rather than waiting until next January?"