Premier's been taking a look at some of the names being mentioned:
Chaplain to the House of Commons and the Queen, The Revd Rose Hudson-Wilkin
Ms Hudson-Wilkin is the first black female chaplain to the House of Commons.
The 52 year old was brought up in Jamaica before moving to the UK in 1985 and is now a vicar in two inner city parishes in east London.
She told The Sunday Telegraph in 2012: "I have no ambition to become a bishop" but is still a favourite.
Canon Treasurer of St Paul's Cathedral, Canon Philippa Boardman
The 50 year old presided over a national service to mark 20 years since women's ordination in the Church of England.
She was made an MBE in 2011 in recognition of her work to renovate an old church in London.
She spoke out when the initial 2012 women bishop vote was defeated.
Dean of York Minster, The Very Revd Vivienne Faull
The 59 year old is the top favourite to become the first woman bishop.
She was one of the first women to be ordained in the Church of England and is a former chaplain to Clare College in Cambridge – the first women the take the roll.
She was named dean of York Minster in 2012, with a staff of 160 and 600 volunteers to coordinate.
Dean of Norwich, The Very Revd Dr Jane Hedges
Once again Dr Hedges was one of the first females to be ordained as a priest.
The 58 year old is the former Canon Steward of Westminster Abbey and Archdeacon of Westminster and just last month was appointed Dean of Norwich.
She's often been seen greeting senior members of the Royal Family at services in Westminster Abbey and made headlines by being the first clergywoman to shake hands with Pope Benedict XVI.
Rector of James's Piccadilly in central London, The Revd Lucy Winkett
Has been described as "among the most talented priests in her generation" by the Bishop of London.
She's an author, former professional singer and has degrees in history and theology.
She's been made canon precentor at St Paul's Cathedral.
The Archbishop of Canterbury Justin Welby has said the first women bishop could be in place by Christmas but it's still unclear who that will be.