Church leaders have been discussing the move for some time and are expected to reveal their decision in July during the General Synod, the national assembly of the Church of England.
The change could face heavy criticism from traditionalists who believe it would undermine biblical teaching.
The Rev David Phillips, chairman of evangelical group the Church Society, told the Sunday Telegraph: "Though one recognises there are very difficult cases, in terms of the public ministry of the Church we should be modelling the standards Jesus set out, which is that marriage is for life. I don't think it's appropriate for bishops to be divorcees."
The newspaper reports the change was agreed at a meeting of the House of Bishops.
A Church of England spokesman said the House considered the issue during a meeting in May after seeking legal advice.
"The House had asked previously for clarification of the relevant legal background and, in the light of that, has now agreed that a statement setting out its approach to these issues should be prepared.
"It is expected that the statement, addressing the relevant legal and theological issues, will be available in July when the General Synod meets."