The mayor has already met with Assistant Chief Jim McDonnell, and Deputy Chief Charles Beck.
All three candidates were chosen by the police commission from a field of 13 candidates.
The mayor is expected to announce his nominee Monday. His top pick then must be confirmed by the city council. The earliest that could happen is Nov. 10.
Bratton officially leaves Saturday for a job in the private sector in New York City.
Some have voiced criticism that the final candidate pool lacks diversity.
President of the police commission John Mack refuted that criticism by saying that the commission considered a wide range of minority candidates.
"The candidate pool that we interviewed included African Americans, Asian Americans, women, Latinos and white males, obviously," said Mack.