The sources told The Santiago Times that the Vatican's Chilean representative began looking into the case of Bishop Marco Antonio Ordenes Fernandez, 47, four months ago.
Ivo Scapolo has been given the task of determining if the allegations are true and whether any other complaints have been made.
Ordenes reportedly stepped down from his post in the northern city of Iquique in August, blaming ill health for his absence from religious events.
He first came to public attention in 2006 when he became the youngest man ever to assume the role of bishop.
Ordenes chairs the Committee on Pastoral and Religiosity Multitudes of the Latin American Ecclesial Conference.