Under the planned counter extremism bill all places that care for children from more than six hours a week would have to register with the government.
They would then be inspected to make sure they are upholding "British values" and not sharing "extremist views".
There is a fear this will lead to state regulation of Christianity and discussing issues like homosexuality or Islam at Sunday school could land a church in trouble.
The Observer newspaper says its source in Whitehall understands the bill will be quietly put aside after a number of government lawyers raised objections.
One issue raised by Christian campaigners was the lack of a clear definition of what extremism and British values were.
It's understood lawyers agreed with this view and warned ministers the bill was not legally acceptable.
The source is quoted by the newspaper as saying: "The bill is sinking without trace. They cannot get a working definition of extremism - lawyers are effectively saying it's incompatible with issues like free speech."
Christian charities CARE, Christian Concern, Evangelical Alliance, Lawyers' Christian Fellowship and The Christian Institute are unhappy at how churches are being targeted.
In a statement, they have previously said: "Requiring churches in England to register before they are legally allowed to help children learn the Christian values our nation was built on is an unjustified restriction of religious liberty.
"Whether the threshold is six hours in any week or higher, the principle of outlawing 'unregistered churches' from teaching children the gospel is an unacceptable overreach of the state."
