Children as young as four will be given the chance to save small, regular amounts of money and gain experience of working as a junior cashier or bank manager.
The plans are part of efforts to help stop them getting into debt or having to rely on pay-day loans later in life.
Parents and school staff can also sign up for the clubs, which would be run by credit unions and reinforced by teaching resources.
The resource pack would also provide advice on promoting Christian values such as generosity, charitable giving and fundraising.
The Archbishop of Canterbury's Task Group on Responsible Credit and Savings has put forward the proposals.
Chair of the task group, Sir Hector Sants, says they want to "transform lives" by establishing a responsible approach to money from an early age: "This programme would also strengthen communities through building links between schools, churches and credit unions, and is part of the Church of England's broader initiative to support the development of a larger, vibrant and more sustainable community finance sector in this country."
The Archbishop of Canterbury, Justin Welby, has also welcomed the plans, saying that how we think about and use money is central to "a fulfilled and contented life": "That is why I strongly support this exciting initiative to encourage children to develop positive attitudes towards money and the habit of saving.
"One in four primary and middle schools are Church of England schools, so this programme has the potential to make a significant difference to the lives of millions of children and future adults."
The task group is hoping to get funding from Government and other sources to carry out a pilot scheme with the Credit Union Foundation and the Personal Finance Education Group.
Six areas are being examined, from which the three will be chosen, in the London, Yorkshire, East Midlands, North East and South West regions.
Hear Tom Sefton, Advisor on Economics Policy for the Church of England, talking about this on Premier's News Hour: