Dr Jeffrey John is believed to be on the list of nominations being considered on Monday and Tuesday by the Crown Nominations Commission.
The orthodox group said the reports were a reminder of the “supreme importance of prayer” over the appointments of bishops, which are approved by the Prime Minister and the Queen.
“Please pray, and encourage others to pray too, that the Holy Spirit will so control the meeting of the Commission that the person chosen is a godly person whose life and doctrine is fully in accord with the Church of England’s teaching and formularies, which means most of all in accord with the teaching of Holy Scripture. Pray also for the clergy and people of the Diocese of Southwark,” it said.
In a joint statement, Anglican Mainstream’s Convenor Philip Giddings and Secretary Chris Sugden said that clergy whose doctrine was not “fully in accord with the Church of England’s teaching and formularies” should not be appointed as bishops.
They warned that if Dr John’s candidacy were approved, it would split the Anglican Communion.
They said: “Given the contested state of the Anglican Communion, an appointment which does not meet those requirements in the Church of England would bring to an end any hope there might be of holding the Communion together.”
Prime Minister David Cameron is reportedly supportive of Dr John’s nomination, which was decided during a recent closed door meeting chaired by the Archbishop of Canterbury, Dr Rowan Williams.
Divisions in the Anglican Communion over homosexuality have peaked since The Episcopal Church in the US consecrated its first openly gay bishop in 2003. That move sparked an exodus of orthodox parishes out of TEC and the formation of a new Anglican body, the Anglican Church in North America.
TEC consecrated its first lesbian bishop this year, to the consternation of Anglican Churches in the Global South who are angry that TEC has failed to respect moratoria on the ordination of partnered homosexuals. The Archbishop of Canterbury responded to the consecration by barring TEC from certain dialogues and meetings.
There are fears that the Church of England would suffer a similar split if it pursues a similar path.
There was acrimony among conservative Anglicans in England as well as overseas, particularly in Africa, when Dr John was appointed as Bishop of Reading in 2003. He stepped down from the post in the face of strong protests and entered into a civil partnership in 2006.
A spokeswoman for the Diocese of Southwark said it was unlikely that the nominations would be publicly announced before the autumn.