A letter detailing the plan, known as "Operation Trojan Horse", claims responsibility for leadership changes at four schools.
These schools are Adderley Primary, Saltley School, Park View School and Regents Park Community Primary School.
Saltley's head teacher resigned last year after a critical Ofsted report.
Inspectors said there was a "dysfunctional" relationship between head teacher Balwant Bains and governors which was hindering the school.
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When the parents have been identified, we start to turn them against the head teacher and leadership team”
A line in the letter
The letter, which purports to outline "Operation Trojan Horse", has subsequently been sent to at least another 12 schools in the city - all believed to be vulnerable to takeover.
It states that parents could be encouraged to turn against the leadership team if they are told the school is "corrupting their children with sex education, teaching about homosexuals, making their children pray Christian prayers and [carrying out] mixed swimming and sport".
Among various claims in the letter is one that the group has "caused a great amount of organised disruption in Birmingham and as a result we have our own academies and are on the way to getting rid of more head teachers and taking over their schools".
The head teachers of the schools met Birmingham City Council on Thursday to discuss their concerns.
The letter, seen by the BBC, was apparently written by someone in Birmingham to a contact in Bradford, and goes on to outline ways and means by which schools can be taken over.
It says:
"We have an obligation to our children to fulfil our roles and ensure these schools are run on Islamic principles."