According to Christian Today, he is one of four men in the running to replace Nigel Stock, who has moved to Lambeth Palace to work alongside the Archbishop of Canterbury.
If he is appointed, he will be the first openly gay bishop in the Church.
In 2003, he came close to being named bishop of Reading, but pressure from then Archbishop of Canterbury, Dr Rowan Williams, reportedly saw him withdraw from the post.
Since then he has become dean of St Albans and has entered into a civil partnership.
A committee from the Diocese of St Edmundsbury and Ipswich will interview candidates before nominating the preferred choice.
The Archbishop of Canterbury and the Prime Minister will then be asked to approve.