Patricia O'Donnell, head of Clarksfield Primary School, Oldham, also alleged she had received death threats.
Oldham Council said it investigated the claims made in December but concluded, in a report leaked to the Sunday Times, it had "no concerns" about any schools.
The report would remain confidential, the council said.
Councillor Amanda Chadderton, cabinet member for education and early years, said: "We take any allegations about our schools very seriously and always investigate in the interests of pupils, staff and parents.
"The report into an Oldham primary school found no basis to 'Trojan Horse' allegations."
The Sunday Times story also referred to a counter-extremism official raising concerns over two other schools in Oldham - Horton Mill and Oldham Academy North.
Ms Chadderton added: "At this time, we also have no active investigations or concerns about any of the other schools the Sunday Times has asked about."
The Department for Education said: "We are already aware of the allegations raised in the report and we are working closely with Oldham Council."
According to Sunday Times article, Islamic teaching sessions were hosted on school premises, a parents' petition was organised against the head teacher and objections were raised to activities including Hindi music being played in class and sex education.
The school - which has more than 450 pupils, predominantly of Pakistani heritage - is rated as "good" by Ofsted.
The National Association for Head Teachers (NAHT) union said it was currently supporting a number of members in the Oldham area with a variety of "Trojan Horse" allegations.
A "Trojan Horse" inquiry in Birmingham centred around anonymous allegations which claimed there was a plot by Islamist hard-liners to take control of several schools in the city.
The allegations sparked investigations by several agencies, including the Department for Education and Ofsted.
A head teacher's claims of a "Trojan Horse" Islamic takeover at a school have "no basis", a council investigation has found.