The decision, reported Friday, was made by the House of Bishops at a meeting in December, The Guardian said. The bishops said they would take no further action until Sir Joseph Pilling, a career civil servant who retired as permanent secretary of the Northern Ireland Office, completes a report on the church's attitude toward sexuality.
The Rev. Jeffrey John, an open homosexual who serves as dean of St. Albans Cathedral, was named bishop of Reading in 2003, setting off a contentious debate. John eventually agreed to stand down and a move to make him bishop of Southwark failed in 2010.
The church said in 2005 celibate homosexuals in committed relationships may serve as priests.
Conservative evangelicals are expected to be angered by the House of Bishops' December decision extended that to bishops.
"That would be a major change in church doctrine and therefore not something that can be slipped out in the news," said Rod Thomas, head of the evangelical group Reform. "It is something that has got to be considered by the General Synod."
The church is already involved in a major row about female bishops. The General Synod narrowly rejected allowing women to become bishops, a change supported by Rowan Williams, the outgoing archbishop of Canterbury, and other church leaders.