Council officials had originally proposed last month to switch buildings to address accommodation issues at the over-subscribed St Joseph's RC Primary and the under-subscribed Broomhouse Primary.
Councillors then put the plan on hold in order to investigate another proposal by Broomhouse parents that would see St Joseph's given extra classrooms in Broomhouse's infant wing.
But officials have ruled against the new option amid fears about the impact it would have on the "ethos" of the two schools – despite admitting it would be a cheaper option.
A new report to go before a special meeting of the education committee found that switching schools would cost 35,000.
The new option of allowing St Joseph's to share some of Broomhouse's space would have only cost 7,800.
Gillian Tee, director of the city council's children and families department, said that sharing space would have "notable drawbacks".
She said: "There are a number of management issues associated with a shared option that would need to be addressed.
"St Joseph's have indicated considerable concern and the extent to which it may erode the school's ethos."
The Evening News reported yesterday that the Archdiocese of St Andrew's and Edinburgh wrote to the council pointing out that, under the 1918 Education Act, it would be able to appeal against approval of the sharing scheme to the Scottish Government as it felt it would lead to a "significant deterioration" in the provision of Catholic education for pupils of St Joseph's.
Ms Tee said an appeal would make it "unlikely" that any changes could be put in place in time for the start of the August 2010 term.
If the swap goes ahead, 20,000 would be made available to allow "essential work" on the schools.
The headteacher and parent council at St Joseph's has supported the swap of buildings.
But in a submission against the swap, Broomhouse parents said it would reduce the school's ability to enrol new pupils from areas of regeneration, such as Sighthill and Broomhouse.
Councillors will decide whether to approve the new recommendations for a swap at an education committee meeting next week.
Councillor Marilyne MacLaren, the city's education leader, said: "We understand that this is a very sensitive issue and we always want to be sure that pupils are at the centre of our considerations."