The councils, which include the Wirral, Lancashire and the London borough of Kensington and Chelsea, are under pressure from growing numbers of parents who want their children to opt out of education at school before 16.
And colleges, which want to increase rolls, are proving increasingly willing to consider accepting teenagers on part-time and full-time courses while they are still within compulsory school age.
Education Otherwise, the home- learning association, reports a dramatic increase in interest among parents in sending children to college and knows of at least 250 under-16s currently being educated by choice in the further education sector. It has worked with some 20 councils which have agreed to pay the fees of children who requested places. Other LEAs have refused.
Local authority associations predict many councils will prove reluctant to fund the teenagers - whose fees are not paid for by the Further Education Funding Council while still within statutory school age - if the trend increases.
The Association of County Councils reported anecdotal evidence of some colleges actively setting out to poach under-16s from schools. But it said financial pressures were likely to prevent many LEAs funding college fees, which would amount to paying twice since they are already obliged to provide school places.
Bryan Davies, Labour's further and higher education spokesman, called for an investigation to gauge the numbers of under-16s actively choosing college. He questioned the implications of the development for the national curriculum if young people could opt out of it. "The whole national debate on what is taught in schools is in the best interests of these young people."
For colleges, under-16s represent a possible new target for recruitment. Many already offer places to under-16s who have been excluded from school, usually using LEA cash. Where no LEA funding is available for self-referred children, some have passed on fees to parents.
David Whitbread of the ACC said cash rather than principle would be likely to prove the main obstacle to wide-scale education authority funding of college places. "Now that colleges are no longer under their control they can see what money they are paying out rather than feeling it is staying within the system."