The 'controversial' vote is part of plans set to boost struggling rural churches.
The proposals will be reviewed next month at the General Synod, which is the Church's governing body.
If implemented, officials from each church would be permitted to preach at the other.
"Acceptance of the proposals would be a profound sign of reconciliation, a healing of wounds that go back to the origins of Methodism in the 18th century," Christopher Cocksworth, the Bishop of Coventry and chair of the Church of England's faith and order commission, said in a briefing document published on Friday.
"The generosity asked of both churches would speak powerfully of a desire for the flourishing in unity and witness of the whole Church of God, and not first and foremost the entrenchment of our own institutions," he added.
However, the plans could prove to be decisive as the proposals would mean Methodist clergy who had not been ordained by a bishop would be entitled to hold Church of England services.
William Nye, the Church of England's most senior civil servant, told The Times bishops felt this was a "bearable anomaly" but others would be "concerned" that the proposal would break the "continuous apostolic succession" that Anglican members believe links their clergy and bishops to the original followers of Jesus Christ.
Similar proposals to bring the two churches closer together fell apart in 1972 and 1980 due to disagreements including over the laying on of hands and whether the Methodist ministers were being officially re-ordained into the Church of England.
However, in 2003 the churches signed a covenant and committed to work towards unity.
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