Schools could be led by business and community leaders, a report for the government suggests.
A union survey suggests over-regulation puts people off headship
Ministers should look at removing barriers to such appointments, although only teachers should be in charge of teaching and learning, it recommends.
The study, by PricewaterhouseCoopers, comes as heads complain teachers are put off applying for the top job by bureaucracy and a lack of rewards.
Ministers say there is no recruitment problem but improvements are possible.
Ministers commissioned consultants PricewaterhouseCoopers to look at the issues around the job of head teacher last year.
Their report says so-called "hero heads" cannot do everything and that responsibilities should be shared more widely.
There will be a need for increased expertise in areas such as finance, human resources, collaboration and project management.
Schools Minister Jim Knight said that the report's recommendations would be fully discussed with the teaching and support staff unions before any action was taken.
He also announced the National College of School Leadership would be given £10 million to support its strategy to help identify future head teachers and cut the time it takes to qualify.
He said: "A modern school requires modern leaders. Many schools will go through major rebuilding work in the next decade or so. They will become extended schools open to the community far beyond the school day and throughout the holidays. This requires new ways of working and a new approach to leading a school.
"Of course, while it may be helpful to a school to have an overall leader with a broad range of skills, I am clear that senior staff with real classroom experience should remain in charge of teaching and learning."
Steve Sinnott, general secretary of the National Union of Teachers (NUT), said head teachers were given an "unending task" because of government initiatives but recruiting from outside the profession was not the answer.
"Moves to divorce the leadership of schools from teaching and learning and replacing heads with chief executives will make things worse," he said.
"If we are to avoid a severe crisis in recruiting new heads, the government must recognise its responsibility for creating the head teacher recruitment crisis."
The government insists there is no problem in recruiting good heads, saying that vacancy rates are low and stable - below 1% of the workforce.
According to a new study for the NUT, teachers are put off from applying for headships by "excessive demands", bureaucracy, external interference and over-regulation.
Money was also an issue, especially in primary schools, with responsibilities not being matched by salaries.
The report said: "The government should look to itself and ask whether its reforming zeal and policy of pressure from the centre is in the best interests of our schools.
"The crisis, if there be one, seems to us to be government-made."
There was little support for moves towards federating groups of schools under one "super head". A majority of those questioned for the NUT report believed the line of responsibility would be confused.
Leaders of head teachers' unions were divided in their reaction to the idea of non-teachers leading schools.
Mick Brookes of the National Association of Head Teachers told BBC Radio Four's Today programme: "We have no objection whatsoever to people who are outside the education arena working with school teams, indeed being school leaders in charge of schools.
"But we think the direction should still come from somebody who has that deep base and understanding about how schools work how children learn and those skills of teaching that you can only get by doing the job."
The Association of School and College Leaders had proposed the idea to PricewaterhouseCoopers.
"We were not saying that people can be brought in from industry to run schools," said its general secretary, John Dunford.
"But the possibility should be opened up that the best of school leaders who are not qualified teachers - the bursars and business managers - should be able to come through to the top job, provided that the person in charge of teaching and learning is a qualified teacher."