The National Governors' Council believes agreement can usually be reached without governors having to relinquish budgetary or policy-making powers.
Education action zones, run by "forums", are expected to boost standards in clusters of poorly-performing schools. The first 12 zones started operating this month.
Forums will include governors' representatives, but the role of governors in zones is ambiguous. They will have to consent to their school becoming a member of a zone, but forums will be able to take on governing bodies' roles and responsibilities.
Pat Petch, chair of the National Governors' Council, said: "We welcome any initiative that's going to put money into schools and tries to tackle both underachievement and deprivation.
"Our advice has been, don't cede your powers because we don't believe it is in the long-term interest of the school community. You could ask the forum to act on your behalf on something without ceding your powers.
"If you cede your functions or powers, there is an issue about the residual legal responsibility. You could be in a position where ultimately you are responsible legally for something but you have handed over decision-making to someone else and are not in a position to fulfil that responsibility."
She said the situation could become complicated over employment law and health and safety issues or in dealing with Office for Standards in Education inspections.
She added: "What we would like to see are the schools working together, retaining their budgets and decision-making powers, but coming to agreements about supporting joint initiatives. You have got to negotiate - then it makes schools stronger."