Candidates for bishop of Southwell and Nottingham are being interviewed on Tuesday and Wednesday.
Applications from women have been considered for the vacancy. After the interviews, a preferred candidate and a second preference will be put forward.
No announcements will be made until 2015 as the appointment needs to be approved by the Queen on the recommendation of the prime minister.
In November, the Church of England formally adopted legislation allowing women to become bishops.
The first women priests were ordained in 1994, but they had not been able to take on the Church's most senior roles.
It has been a divisive issue for the Church - some Anglicans feel the move is consistent with their faith but the traditionalists disagree.
In November the general synod, the Church's law-making body, gave the final seal of approval to the legislation, which had passed through Parliament in October.
The vacancy in Southwell and Nottingham arose after Bishop Paul Butler left to become the Bishop of Durham in January.
Gloucester, Oxford and Newcastle are among the other dioceses where new bishops will soon be appointed.
The first woman bishop in the Church of England could be selected this week.