The churches already jointly run two schools on the island.
Now that co-operation is likely to be developed further with the Rt Rev Philip Egan, the Catholic Bishop of Portsmouth, and the Rt Rev Christopher Foster, Church of England Bishop of Portsmouth, launching an eight week long feasibility study into creating a joint Anglican/Catholic scheme covering all their other schools on the island.
The Catholic Diocese of Portsmouth has announced that it expects all four of its schools there to join the scheme.
The governing bodies of some of the 11 Church of England schools have also expressed an interest in the idea.
There are also a number of separately-run community schools on the island and if the Anglo-Catholic project is eventually given the go-ahead, they could also be invited to join in.
Church officials insist they would not be asked to become C of E or Catholic academies as a condition on joining.
Anyone who has any views about the proposals can email them to the two Dioceses of Portsmouth.