Glasgow City Council said it had already held discussions about changing the catchment area of Hillhead Primary, in the west end.
The move would be controversial because families who have bought properties in the area to secure automatic right of entry to the school for their children may find themselves outside the catchment area.
The move comes after the parent council warned that space problems at the school were becoming "critical", with urgent action required to prevent problems escalating.
On Saturday families living in the catchment area who had enrolled their children in P1 were told they no longer have an automatic right to a place because the school is over-subscribed.
Hillhead has space for 99 pupils starting in P1 in August, but 121 children have been enrolled, meaning 22 will miss out.
A council spokeswoman said: "Senior officers have been holding informal meetings with parent councils in the area to discuss the catchment areas. The formal consultation would not take place until April or May."
The situation has highlighted the growing problems of over-crowding at the Gibson Street school, which opened three years ago after a merger with other primaries.
The school was built with a capacity of 632 pupils, but has 649 and this is likely to rise to 678 by August.
In the past, the council has said the problem is a result of the popularity of the school as well as rising population trends.
The Scottish Government's move to legislate to cap numbers of children in P1 classes at 25 has also restricted flexibility.
However, opposition politicians says the council's school rationalisation programme has under-estimated the number of places schools will need. They have also criticised Glasgow's decision to increase numbers so rapidly by taking children who do not live in the catchment area, despite warnings over the impact on its facilities.
The school has already lost its dedicated art room and music room, which are now being used as classrooms and there are plans to convert its library into a classroom.