Sir John Cass Foundation and Redcoat school in east London has previously been graded 'outstanding' by Ofsted.
According to the Independent newspaper, the education watchdog carried out a number of unannounced inspections at schools in the Tower Hamlets area, and reduced its rating over concerns about a sixth-form Islamic group.
It is claimed that the student society's Facebook page had links to a radical preacher and also set up an unmonitored YouTube channel.
In reports, due to be published on Friday, it is expected to be revealed that the school in Stepney failed to properly safeguard students.
Six other independent Muslim schools in the area are also reportedly understood to raise 'safeguarding issues'.
The inspections, which were carried out at a total of seven schools, with no advanced notice, were allegedly carried out at the request of the Department for Education, following the 'Trojan Horse' allegations that schools in Birmingham were being targeted by extremist Muslims.
Despite being a C of E school, the intake of students at Sir John Cass is 80% Bengali Muslim (which reflects the makeup of the local community), with just 18% of places going to pupils from a Christian denomination.
Tower Hamlets council says it will not comment until the school's reports are published.
But the council's corporate director of education Robert McCulloch-Graham is quoted as saying: "As is common practice, we will work with the leadership of this school to address any issues identified by Ofsted.
"As a local education authority, we have no jurisdiction whatsoever over teaching and standards at independent faith schools. This is Ofsted's area of responsibility.
"We do, however, have responsibility for safeguarding all children in the borough and have always exercised our safeguarding duties to the full.
"We are working closely with Ofsted and the Department for Education after their recent inspections and we will of course act on the findings of the reports. We will continue to work with Ofsted and the DfE to address any issues, potential or otherwise.
"The council and its partners have worked extremely hard to build the cohesive community that is Tower Hamlets and will do whatever is necessary to ensure that this continues."
"We note that of the schools inspected, only one is a publicly-funded maintained school."