In the draft document 'Needs Analysis Report', the church says "recruitment of school leaders with the necessary understanding and commitment is proving increasingly difficult, and sometimes impossible.
"Many dioceses have become more flexible around the requirement that headteachers need to be practising Christians and can reference successful church school heads who are from other faiths or none at all but are able to maintain a clear vision for education."
However the Church is concerned over the long term ramifications of not having heads from a Christian background.
It says it wants to give more support to schools and dioceses to help them: "In the long term there is a risk to the vision if sufficient numbers of teachers and school leaders with a deep understanding of and engagement with the Church of England cannot be deployed."
While the document is widely available online, the Church of England have refused to comment directly on what it says, instead choosing to release an in house interview with its Chief Education Officer Revd Niger Genders. In the interview he discusses the need to give further support to schools on the issue of training new leaders.
He said: "Both community and church schools increasingly testify to difficulties in recruiting headteachers and our recent consultation has shown a strong desire for more support in training new leaders.
"They say that the training that they're provided with doesn't always help them to focus on those broader issues, that it tends to be narrowed to just thinking about particular things which they will be held accountable for rather than this broader vision for a hugely diverse and encouraging education, which they can give to all of their children."
While the Church looks at how to improve recruitment, a former headteacher of a Christian school has told Premier it's important a head can follow the ethos of a school.
Speaking on Premier's News Hour Tim Crow, now a trustee at the River School, said: "The head and as far as possible the staff - ought to embody that.
"I think if [parents] have chosen a Christian school - one has to ask why are they choosing that school?"
He added that in his own school: "We made it very clear that it was a Christian school and they would choose it on those Christian values."
Listen to Tim Crow speaking to Premier's Antony Bushfield on the News Hour:
Listen to the Church of England's released interview with Revd Nigel Genders here:
