Lee was left with picking the department's top cop after outgoing Mayor Gavin Newsom appointed Chief George Gascon as district attorney in January.
Gascon's second in command, Jeff Godown, is serving as interim chief.
The police commission whittled down a list of applicants and submitted three candidates to Lee a month ago.
But Lee's choice may serve only a short term because voters will elect a new mayor in November, and the winner is free to name his or her own chief.
