It is understood that the plan, which emerged from meetings between Archbishop Welby and the Pope in June, will focus on how both Churches can work together to help those in poverty around the world.
They will also speak out together to challenge governments and international authorities.
The Holy See rarely issues joint statements so it will mark a new development in Catholic-Anglican relations if both Churches act together.
Archbishop Welby revealed he was working on a joint initiative with the Pope during the Church of England's General Synod, but would not be drawn on details.
At their meeting in June, both men talked about the need to build a fairer global economic system.