Broomhill Primary School, in Hyndland, Glasgow, could be demolished to make way for a state-of-the-art building on the same site.
But local politicians have expressed concern that the school may not be large enough for the growing population and there are worries that neighbouring land could be lost.
Local MSP Bill Kidd said: "I am delighted that the new build for Broomhill Primary School looks likely to receive the go-ahead. But I am conscious that there are concerns regarding the number of classrooms, as this is a very popular area that has shown signs in the past couple of years of attracting a lot more young families. There are also serious concerns about the eventual fate of the land that presently holds the annexe."
Councillors will debate the proposals for the school at an executive committee meeting today.
Councillor Stephen Curran, executive member for education and young People said: "The consultation process is the ideal way for any one in the local community to give their views on the proposals."