A new school will be required in Glasgow to keep up with demand given the two existing primaries are already full.
At present, 900 pupils are in Gaelic Medium Education (GME) in Glasgow, where pupils are taught the majority of lessons in the language, with rolls predicted to increase to 1150 within three years.
A paper to the council’s education committee said a “sharp increase” in demand for places had been recorded in August 2016.
The report said: “With primary provision growing, secondary provision also needs to grow.
“The current sustainable P1 intake across both GME primary schools is 85. This is considerably fewer places than the current demand.”
It concludes: “It is accepted there is a need for a third school for uptake of GME to be maintained at current levels, never mind expand.”
However, the paper also warns of a shortage of Gaelic teachers across the country, according to a report in the Evening Times.
Recent Scottish Government statistics showed pupils in Gaelic primary schools are doing better at reading, writing, listening and talking at nearly every stage of primary.
More than 6,000 children were in GME education across Scotland in 2016 with Glasgow the biggest provider outside the Highlands and Islands.
Councils are now obliged to investigate the case for a Gaelic unit whenever parents ask for one.
Only one in five GME pupils have Gaelic-speaking parents.
Local authorities have complained that the legislation puts further pressure on the education system given a lack of funds and low numbers of qualified teachers.
Government figures, published in February, show the proportion of Gaelic-educated P4 pupils achieving expected levels in reading, writing and listening and talking were 79 per cent, 76 per cent and 87 per cent respectively.
Equivalent figures for non-Gaelic pupils were 75 per cent, 69 per cent and 81 per cent.