If they make it onto the approved list, authorities could find themselves taking over the duties of rival councils judged to be struggling.
The Local Government Association is urging all education authorities to apply for a place on the list - and the opportunity of running services such as admissions and pupil welfare.
The LGA wants to take advantage of plans to hive off council education services. Adverts seeking contractors were placed in the press by the Department for Education and Employment this week.
Graham Lane, the LGA's education chairman, believes few other organisations will be able to compete with the expertise available within local government.
Both the LGA and his own authority of Newham in east London - which last week received a good inspection report from the Office for Standards in Education - are bidding.
"If we can make some money on it we can put it back into our schools," he said.
But Bury, another highly praised authority, is holding back.
Commercial companies and councils may have to see off competition from the voluntary and schools sectors. Rathbone CI, which works with young people at risk of exclusion, is interested in contract work - but the Prince's Trust, also involved in exclusion prevention work, is not.
"We already work in partnership with education authorities. We don't do it for profit," said Rathbone CI spokeswoman Carol Toms.
Kingshurst City Technology College, Birmingham - on the short list to take over a failing Surrey school - is interested. Independent schools are another source of potential contractors.