The school, sited at Bellahouston Academy, is a key element in the council's strategy to create specialist centres while removing hundreds of redundant places. The education department invited all city primaries to nominate pupils with a special aptitude in swimming, hockey or gymnastics.
They set a target of 20 places. But only 14 of the 28 applicants have been offered places.
Six of those declined to take them up. Two of the remaining eight are from East Dunbartonshire and will be treated as placing requests. There are no swimmers among the eight, although four swimmers turned down places.
Jim Cassels, Bellahouston's headteacher, said the disappointing response may have been partly due to the fact that pupils specialising in sport would be restricted to a maximum of six Standard grades and three Highers. Parents may also have been reluctant to separate their children from friendships made at primary school.
An education department spokesman said that the numbers were less than hoped for, but could be ideal for getting the sports school underway. Other activities, such as athletics, could be offered later - perhaps when the first group reached their third year.
"We set very high standards in this instance and it is possible that we erred on the side of caution. We will learn from this as the school develops," the spokesman said.
The Educational Institute of Scotland has voiced concern over the restricted academic options for pupils and the use of staff who are not registered teachers.
Willie Hart, Glasgow EIS secretary, said: "We had strong reservations about the sports school concept. But now that the council has taken the decision to go ahead, we will attempt to ensure that standards of professionalism are maintained and teachers' conditions are protected."
Mr Hart said certain matters remained outstanding, especially the use of sports coaches. "It is a fundamental issue to us that during the school day coaches should not replace teachers. They should work in conjunction with professional educators," he said.
The EIS nationally is being kept in touch with developments and an approach to the General Teaching Council is possible.