Sir Cyril Taylor, chairman of the Specialist Schools and Academies Trust, said police faced problems in areas where different communities were concentrated in separate schools.
He suggested that such "segregated" schools should be replaced with privately sponsored academies.
Bradford and Leeds were among the areas where such changes could be implemented, Sir Cyril said.
But his comments were severely criticised by one senior Bradford councillor who described them as "staggering" and unfairly singling out Muslims.
David Ward, a Liberal Democrat who was formerly executive member responsible for education, said: "It's frightening that someone who has the ear of the Prime Minister has these kind of views. He's stoking up the prejudice that already exists in many parts of the country."
And Leeds City Council said it was nonplussed by being included in Sir Cyril's plans given that it doesn't have any schools dominated by a minority group.
Sir Cyril said: "We have a huge number of children in this country in schools which are, in effect, segregated. Hopefully, most people agree that that is not a good thing.
"How do you then resolve it? Obviously we have to do so by agreement. You can't enforce quotas on people or change catchment areas arbitrarily.
"But if you set up an academy programme it can be done on a multi-faith basis and if you have got agreement there is a good chance it will work."
One project is already planned in Oldham while it is hoped that the approach could spread to other "areas where ethnic minorities, especially Muslims, are concentrated", including Bradford, Tower Hamlets in east London, Blackburn and Leeds.
Sir Cyril said that the police faced "a real strategic security problem" in some parts of the country where, for example, children only speak Bangla at home and do not mix with other communities.
He said that where an area has two schools, one dominated by children from Pakistani backgrounds and the other mainly white, they should both be shut down and put together in a new academy.
However, the Department for Education and Skills said: "Any suggestions of closing schools are wide of the mark. However, all schools can and should play a leading role in creating greater community cohesion."
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