The revelation from community group Al-Madinah, formerly known as An-Noor Institute, has sparked fears of poor standards from unions and campaigners.
The group wants to build a primary and secondary school on a site to be found in Normanton.
It has been given approval under the Government's Free Schools scheme, which enables any group to start a school without permission from local councils.
The Department for Education also allows such schools to use head teachers and teachers without official qualifications.
Ziad Amjad, project organiser for Al-Madinah, said the schools might need to take advantage of this for Islamic studies teachers.
He said: "We will look to find qualified teachers to fill these roles but they are difficult to find. If we do employ unqualified teachers we will fund their training so they can get those qualifications. The quality of teaching does not just depend on what qualifications you have, it also depends on quality of knowledge and that will be very high."
Mr Amjad said the school would employ qualified teachers for its other subjects and a head teacher with a National Qualification for Headship even though these are not legal requirements.
He said the amount of Islamic Studies lessons that would be held was still under discussion but it would probably be "two or three" a week.
Dave Wilkinson, Derby branch secretary of the National Association of Schoolmasters and Union of Women Teachers, said his organisation's national policy was to dissuade parents from sending their children to free schools. He said: "You could end up with children being taught in what are very controversial schools by unsuitable people.
"Teaching religious studies in any form is a skilled subject. It should be taught in the context of respect for other faiths or you risk building up tension in different communities. Our fear is that this might not happen here."
The Derby Campaign for Inclusive Education (DCIE) is against the schools plan as it says it is better for children to learn together, regardless of their faith.
Mike Lake, one of the campaign's founders and a former teacher, said since the Government was spending taxpayers' money on such schools, teachers should be qualified.
He said: "I don't think you can just walk into a classroom and teach. I have nothing against unqualified people coming in to give talks, but with teachers' supervision."
As previously reported, the Government's Partnerships for Schools is helping Al-Madinah look for a suitable site in Normanton.