The Catholic Church in England has told its schools it would be "unwise" for them to apply for academy status.
The government has written to all schools in England inviting them to become academies - billed as independent state schools.
The Church of England has said it would not object to its schools seeking academy status.
About one third of schools in England are faith schools and most of those are Christian.
The Catholic Education Service has written to 2,000 Catholic schools, advising "great caution" on academies.
Chief executive Oona Stannard said under the plans, land and property of an existing school would transfer to new academy trusts.
Much of the land and buildings of Catholic voluntary schools are owned by church dioceses or religious orders.
They would be unlikely to agree to give up these assets, said Ms Stannard.
At the moment, Catholic schools receive 90% of their funding from the state and 10% from church funds.
They already have some of the freedoms being offered by the government to schools which want to become academies, such as control over their admissions.
Ms Stannard warned: "The funding opportunities may initially seem attractive to schools but remember there is, as yet, little precise detail on this and the payment of our 10% to capital costs at present buys our sector a degree of valuable independence along the lines of "he who pays the piper calls the tune".
"We would be very unwise to trade this for an uncertain future and a higher level of risk."
Schools opting for academy status will receive a budget uplift of about 10% - money normally kept back by local authorities to provide special services such as help for children with special educational needs, admissions and provision for excluded pupils.
The Church of England is less cautious about the academies plan and has yet to give guidance to its schools.
Its education chiefs have been talking to Education Secretary Michael Gove.
A spokesman for the Church of England said: "We broadly support the purposes of the Academies Bill, but there are some technical concerns about elements of the proposals.
"We would not object to Church of England schools taking up the opportunity to convert to academy status, but we would encourage them to consider carefully questions such as whether academy status will directly benefit students and their families, and whether becoming an academy might undermine equitable distribution of resources to other schools.
"We anticipate that many local Church of England dioceses will grant conditional approval to schools seeking to convert, with governance conditions being set out to guarantee that the school will continue to develop a Christian ethos."
The bill which will pave the way for schools to become academies is currently in the House of Lords.
It is expected to become law before MPs break for the summer, the idea being that some top schools could become academies in the autumn.
Mr Gove has said 1,700 schools have so far expressed an interest in becoming an academy.
Schools judged by Ofsted to be "outstanding" will be the first to transfer.