Downing Street will make the announcement at 10am, after the Queen approves the appointment.
They will replace Bishop Michael Perham (above), who retired from the role last November following two allegations of indecent assault.
He was interviewed under caution but was not arrested and police have since said no further action will be taken.
The job is a Diocesan bishop and anyone in the role would be able to take a seat in the House of Lords.
If the position is given to a woman that would mean the first Church of England female bishop could take her place in the upper chamber as early as July.
A male bishop in the diocese would have to wait several years to enter the Lords but a change in the law means women are fast-tracked.
Female bishops are now first in line to succeed current "Lords Spiritual" members of Parliament when they retire.
The Diocese of Gloucester has been known for its open stance in favour of women bishops.
