Schools would be run more independently under the scheme
East Lothian has said it is considering becoming the first council in Scotland to allow schools more independence.
Residents are to be consulted on a council proposal to set up an arms-length trust to run schools.
Head teachers have revealed they feel frustrated in their attempts to raise standards because they have little control over areas such as spending.
David Berry, the council's leader, said organisations are better managed if they are not centrally controlled.
Mr Berry said the idea also stems from concerns over expected massive cuts in public spending.
The council stressed it has no plans to replicate the exact structure and status of trust schools in England.
If the East Lothian proposal is approved by residents and other councillors any changes would take at least two years to implement.
A Scottish government spokesman said: "The Scottish government supports councils giving greater flexibility and control to schools and headteachers, to exercise good leadership and management.
"However, this does not mean the adoption of the arrangements that exist for trust schools in England."
A spokesman for the Educational Institute of Scotland, the main teaching union said: "While the East Lothian proposal currently appears to be highly speculative and lacking in meaningful support, the EIS would have serious concerns about any potential return to the failed opt-out type policies of the past.
"It is already difficult to recruit headteachers in schools, without adding yet another responsibility to the job and removing the established local authority support.
"At a time when many schools are already suffering as a result of financial cuts, asking headteachers to take on additional financial responsibility over diminishing budgets would only add to the pressures upon them."