The moves come just nine months after the decision by David Blunkett, the Education and Employment Secretary, to give grant-maintained status to two Islamic primary schools.
Plans being mooted in Birmingham and Bradford centre on gaining voluntary-aided status - and 85 per cent of funding - for the Muslim secondary schools.
In Birmingham, the eight existing independent Muslim schools, backed by the Association of Muslim Schools UK, are campaigning for a centrally located co-educational secondary.
It would be purpose-built and could be run by one headteacher, governing body and staff with two single-sex halls and boys and girls taught separately.
In Bradford, the private Feversham College for girls has acquired a former Roman Catholic high school.
The application is being prepared by the Muslim Association of Bradford with the backing of the local authority.
A site has not yet been identified in Birmingham and although both proposals are in their infancy, councillors have agreed that Tim Brighouse,the city's chief education officer, pursue discussions.
Some 1,500 pupils in Birmingham currently attend the private Muslim secondaries, paying fees of between Pounds 500 and Pounds 1,300 a year.
And in a report to education councillors, Professor Brighouse says: "Given the existence of aided schools from other faiths, it is difficult to resist the argument for a Muslim-aided secondary school."
Details of the Birmingham proposal have emerged in his just-published response to the review of secondary education in the city, which has recommended making Park View school girls only to meet the demands of Asian parents for single-sex teaching.
But discussions on greater co-operation between the state and private schools have been taking places between the council and the Muslim community for two years.
Muslim groups fought for 15 years to win state funding for their schools,before achieving success in January when grant-maintained status was approved for two primaries - Islamia in London and Al Furqan in Birmingham.
Previous applications were turned down by the Government for reasons ranging from surplus places, to concerns about the curriculum, financial viability and inadequate school buildings.
Ibrahim Hewitt, development officer for the Association of Muslim Schools UK, said: "Having now got the precedent of Muslim schools within the state system gives us a bit more optimism but our dealings in the past have shown us that most obstacles are at a local level."
Under the Schools Standards and Framework Act, decisions on new schools now rest with the locally appointed schools organisation committee, whose members will include representatives from the council and churches.
The Birmingham proposal has already provoked hostility among local Conservatives. James Hutchings, their education spokesman, said: "In this city we have remarkable tolerance on race and religion and most of that success is based on integration in schools.
"We would be deliberately building apartheid with the development of this school instead of harmony and this apartheid would gradually develop into social unrest and a lack of social cohesion."