An official report on the status of homosexuals in the Anglican Church outlines the case for greater tolerance, according to reports.
The appointment of Canon John threatened a split in the church
The document says Christians share fundamentals such as faith and baptism, rather than beliefs about sexual conduct or blameless personal behaviour, the Sunday Times says.
The Church told BBC News Online the leaked report did not contain any conclusions and was simply "a document providing information for discussion".
But opposing wings of the Church have been quick to comment, with liberals suggesting a compromise is possible and evangelicals demanding clarification that same sex relationships are "always wrong".
The leak follows weeks of fierce debate, prompted by the decision to make gay cleric Canon Jeffrey John the Bishop of Reading - a post he has since declined.
Church leaders had already called for a debate on homosexuality to be delayed until the report was officially published later this year, allowing time for reflection on the issue.
The working party responsible for the report, called Some Issues in Human Sexuality, was headed by Bishop of Oxford Richard Harries - who first nominated Dr John as a bishop.
The Bishop of Hereford says many Anglicans want an 'inclusive' Church
It reportedly says: "What makes us Christians is our common relationship with Christ, which is rooted in repentance, faith, baptism and the gift of the Holy Spirit, and not the correctness of our beliefs about matters of sexual conduct or the impeccability of our own behaviour."
It will also argue for "legitimate diversity" of beliefs, including those held on homosexuality, the Times reports.
But the BBC's Religious Affairs correspondent, Robert Pigott, says the plea for Anglicans to agree to differ may be hard to sell now that the row over Canon John has polarised opinion in the Church.
On Sunday the Bishop of Hereford, the Right Reverend John Oliver, told BBC One's Breakfast with Frost programme the report could provide the framework for setting out the Church's position on the issue.
Suggesting that a compromise was possible, he said: "It's a bit like the way in which Christians have lived with deeply divided views over pacifism and war. We managed to live together, though we interpret scripture in different ways."
He said there were "very many people who long to see a generous, inclusive Church".
Evangelical members of the Church were less enthusiastic about the calls for compromise and the possibility that opposing views on homosexuality could live side-by-side.
The Church Society's George Curry said: "You can't have a clergymen as a bishop, as a leader, who has never repented of their immoral lifestyle and who will be teaching that such an immoral lifestyle is acceptable."
He added: "The Bible tells us that just as adultery is always wrong, so same sex relationships are always wrong."
On Saturday a meeting by the General Synod, the Church's governing body, was interrupted on Saturday by gay rights campaigner Peter Tatchell.
Mr Tatchell accused Dr Williams, of "betraying his own principles" and told the synod he had "bowed to pressure from theological homophobes".
Richard Thomas, director of communications for the Oxford Diocese, told Mr Tatchell: "I can tell you now that he (Jeffrey John) would not approve of what you are doing and he would want you to withdraw."