The historic transfers, which follow parental surveys in 43 areas, is a step in reducing the Catholic Church's dominance in primary education and to give greater choice of school ethos.
Mr Quinn wants the bishops to provide the names of schools to be transferred by the end of this year, to allow time for arrangements for them to open under new patronage in September 2014.
But a church education spokesperson said the situation varied from one community to another and said "practical problems" were emerging in some areas.
Fr Michael Drumm, executive chairperson of the Catholic Schools Partnership (CSP), said in this situation "there is no one size that will fit all" and there would be a need for a creative response to complex situations.
Fr Drumm outlined the church's substantive response to the minister's initiative in an address to the Catholic Primary School Managers' Association (CPSMA) over the weekend.
He stressed that "in all of this, it is imperative to reassure local communities that no change will be implemented without widespread support in the area".
The areas involved have between three and 16 primary schools, predominantly Catholic, and the bishops have been asked to hand over one in each area, generally to allow for the opening of a multi-denominational school.
In practical terms, it would mean the direct handover of an existing school – likely to be met with strong resistance in local communities – or two schools amalgamating first in order to free up a building.
Fr Drumm said that in seeking to respond to the limited request for change in different areas, "attention must be given to the large majority who have expressed no such interest.
"An issue that will arise in many of these areas is the level of displacement that may be required in trying to cater for the views of a minority who want change," he said.
He said the best way forward was through amalgamations.
He
would not be drawn on how many schools he thought would be under new
patronage by September 2014, but said in areas of high demand for
change, plans could definitely be in place by then, but where demand was
low, a creative response would be needed.
Fr Drumm said
that in the individual areas surveyed, between 0.6pc (Roscrea, Co
Tipperary) and 8pc (Portmarnock, Co Dublin) of parents with children in
schools said they would avail of another form of patronage.
He
pointed to Ballina, Co Mayo, where parents of 44 children, or 2.2pc of
pupils currently in primary school, said they would avail of a
multi-denominational school if one was available.
"Anyone
can see that responding to this level of demand will not be easy
because these 44 children are probably scattered across 16 schools. This
situation is replicated in many other areas".