Ewan Aitken, the council's executive member for education, describes the move as "extremely ambitious". It follows the visit of a delegation which he led earlier this year to the American state of Maine which provides Apple iBook computers for teachers and every student in grade 7, the equivalent of P7 and S1. It eventually aims to extend this to all pupils from grade 7 upwards.
Mr Aitken said: "We need to look at the feasibility of introducing a similar initiative in our area but obviously in a Scottish context. The next step is for a group of professionals to look at our needs, the costs involved and the technology which would best suit our pupils and teachers."
Roy Jobson, the city's director of education, will report to next week's council executive, which is expected to endorse the plans, that the group found the Maine trip "inspirational".
The ratio of one computer per student is seen as a key element in the success of the Maine project, which has seen improvements in motivation, attendance and attitude. It reports that grade 7 and grade 8 students with individual laptops demonstrate "higher order thinking skills, collaborative learning and self-paced learning".
Edinburgh's intention is to start by issuing a laptop to all primary pupils and teachers and, as funding allows, extend it to every secondary school student and teacher. The city has yet to put a figure on the funding it needs but it acknowledges it cannot afford to implement the plan on its own.
It would have to seek backers ranging from European sources to the Scottish Executive, which is currently supporting a pilot laptop scheme in schools in Dundee.
An iBook starts at pound;800 which would imply a cost to Edinburgh, just for secondary pupils and teachers, of more than pound;17 million.
The plans have received qualified support from Iain Whyte, leader of the opposition Tory group, who went on the Maine trip. He said there was little doubt it had advantages for pupils, but says a number of potential benefits have still to be proven and suspects that the real benefits come from excellent and enthusiastic teaching.
Mr Whyte said: "My conclusion was that if we choose to believe the increasing body of evidence in favour of one to one schemes, we must make careful measurements as we implement it."