Bishop Michael Perham announced he was quitting with immediate effect on Friday and Premier understands he voluntarily attended a police interview on Tuesday.
Detectives are investigation two allegations of indecent assaults involving a child under the age of 18 and a women over that age in the early 1980s.
He was not arrested or charged.
The Diocese of Gloucester has confirmed the Bishop of Tewkesbury has taken over Bishop Michael's role.
The Rt Revd Martyn Snow has written an open letter in which he says he's saddened by Bishop Michael's resignation.
"I know that, like me, you will have been deeply saddened by this news.
"Various news outlets are carrying a story that this is an investigation by the Metropolitan Police into allegations of indecent assault on a child aged under 18 years and indecent assault on a second female aged over 18 years.
"The police have confirmed that no arrest has been made. You will all realise that this is therefore a traumatic time for Bishop Michael, his family and for those who have made the allegations. Please hold them in your prayers.
"I am sorry that we have not been able to say more until now. I know many people have found this frustrating but I hope you will understand our reasons for this and will appreciate that we have been liaising very closely with Lambeth Palace." He said.