All children should pass their fifth birthday before starting school to ensure that younger pupils do not fall behind and to help cash-strapped local authorities save money, according to a national parents' organisation.
Education directors have admitted that they are increasingly willing to entertain such radical ideas, since all "easy" cuts have already been made.
Although mandatory schooling in Scotland runs from the ages of 5 to 15, local authorities can allow children to start P1 earlier and some pupils begin school at only four and a half years old. Raising the starting age would be a "pretty obvious and straightforward" improvement, said Eileen Prior, executive director of the Scottish Parent Teacher Council (SPTC).
Ms Prior's views were shaped partly by the experience of her son, a December baby who started school aged 4 and was one of the youngest in his class. "There was a sense right through primary school that he was just that wee bit behind," she said.
The SPTC proposes the idea in a submission to the Scottish Parliament's Education and Culture Committee on the 2015-16 draft budget. A higher starting age "would reduce costs and improve outcomes for children at a stroke", the submission says.
"High-quality preschool care costs less than school education and it has been argued that, as well as saving money, it would provide children who otherwise enter school aged 5 with a better start to their education, with long-term benefits," it adds.
The idea was inspired by a new book from University of Edinburgh senior teaching fellow and former secondary headteacher Daniel Murphy. In Schooling Scotland he argues that the starting age should be raised to 5 immediately.
"By ensuring that larger numbers of children are better ready for schooling, this change may have the largest positive effect on the schooling experience of the largest number of pupils of any action government might take," Mr Murphy writes.
He also wants the "two-stage leaving date" to be abolished. This involves many 15-year-olds having to stay on until Christmas of S5 when they would have preferred to leave school the previous summer and is a knock-on effect of children starting school at 4.
What he describes as the "historical anomaly" of Christmas leavers has long caused headaches for schools, as they try to work out what to do with pupils who are keen to leave and do not have the motivation of end-of-year exams.
Edinburgh Napier University research from 2010 shows that these students - about one in 10 of leavers - are "significantly more likely" than their peers to leave school with no qualifications (bit.lyWinterLeavers).
Earlier this year, TESS reported that education directors' body ADES believed councils had exhausted obvious savings and would soon have to explore more imaginative ways to save money. Nothing was off the table, it said - including changing the school starting age.
In ADES' written evidence to the education committee last week, general secretary John Stodter reiterated that all "easy reductions" to education services had already been implemented and that the time had come for "system-wide change".
However, the Scotland Institute thinktank argued earlier this year in its report Early Start 4 Scotland (bit.lyEarlyStart4Scot) that the starting age should be lowered to 4. It said this would help to close the gap that leaves many children from poorer backgrounds trailing far behind their peers educationally even before entering P1.
A Scottish government spokesman said: "We have no plans to change the system for the primary school starting age in Scotland. The current system allows flexibility as to when a parent wishes their child to start school, as not all children are ready at the same time.
"Curriculum for Excellence is now in place to provide a better and more flexible curriculum for pupils from the ages of 3 to 18."