Canon law and guidance in marriage should be interpreted in a way that provides "maximum freedom" for homosexuals, a document from the House of Bishops says.
A comprehensive report following years of discussions on sexuality says new teachings on marriage and relationships should be drawn up to replace those introduced in the 1990s.
There was also "some support" in the House for the new document including "penitence for the treatment some lesbian and gay people have received at the hands of the Church".
Questioning of "ordinands" - priests in training - should change so the same questions are asked of all candidates regardless of their sexual orientation, the Rt Rev Graham James, Bishop of Norwich, told reporters at a London press conference.
But he said the change was not a church version of "Don't Ask, Don't Tell", the former US military policy between 1994 and 2011 which barred openly gay or bisexual Americans from serving but did not discriminate against them if they did not disclose their sexuality.
Bishop Graham said "present arrangements for asking ordinands and clergy about their relationships and lifestyle are not really working very well".
He added: "All clergy are asked at their ordination whether they will fashion their lives 'after the way of Christ'.
"We believe we should revisit how this is explored beforehand so the same questions are addressed to everybody without distinction.
"This is not Don't Ask, Don't Tell in any shape or form."
Recommendations must now be discussed at the General Synod in February.
Bishops said there was "little support for changing the Church of England's teaching on marriage".
The Bishop of Norwich Graham James said this was not the end of the process but left the Church "somewhere in the middle".
"This is no last word on this subject. For there are very different views on same sex relationships within the Church, and within the House of Bishops, mainly based on different understandings of how to read scripture," he said.
The report also speaks of the need for the Church to repent of the homophobic attitudes it has sometimes failed to rebuke and affirm the need to stand against homophobia wherever and whenever it is to be found.
In a foreword to the document, the bishops recognise "that this report may prove challenging or difficult reading."
The General Synod will discuss the paper in a "Take Note" debate on the afternoon of Wednesday 15 February.
