They would be appointed by local education authorities and offered to schools as vacancies arose, but schools would retain the final decision on who would work for them.
The proposals come in a report from the National Union of Teachers Cymru on improving school funding arrangements in Wales. It comes three days after opposition Assembly members voted in favour of a special committee to look into school budgets.
The NUT Cymru report proposes a new teaching and learning grant to cover the core work of delivering the national curriculum, including staffing costs.
The grant would ensure schools in Newport received the same as those in Flintshire for educating a seven-year-old or a GCSE student, taking into account deprivation or Welsh-medium provision.
Local authorities would have to pass this money direct to schools. But councils would retain responsibility for school buildings, special educational needs, school transport, funding for pupils in sparsely-populated areas, advisory services - and professional development and support.
Gethin Lewis, secretary of NUT Cymru, said: "If there were concerns about teaching and learning, you would blame the Assembly. If it was about the condition of premises, special needs or school transport, blame the LEA."
Employing teachers centrally would particularly benefit those in small primaries. Since schools took over appointments in 1998, teachers have moved less, says the union. LEAs could encourage them to broaden their experience and develop their careers.