Open meetings are happening this week, aimed at gathering public input into the process.
Residents shared some of their concerns last night at the Scarborough Civic Centre, where the first of four public consultations was held.
Mukherjee told CBC News the board will not restrict their search to internal candidates. He said the board wants a candidate who will bring a "commitment to innovative practices" with a particular eye to finding ways to curtail rising policing costs.
"There is no preferred candidate," said Mukherjee. "The board wants to be able to consider a short list of very strong candidates. They may be internal, they may be external. We are interested at looking both in Canada and outside Canada. We want to make sure Toronto gets a very good chief."
He also said the public consultations will provide crucial input as the board moves toward a hiring that is expected to happen in February for a term that starts at the end of April.
"We learned from the sessions we did last time and we found they were very beneficial," said Mukherjee. "The input we received from the public was very helpful to us in deciding what we were going to be looking for."
Blair served two five-year terms and sought a third but the board — which provides civilian oversight over the force — opted instead to seek a new chief.
The new candidate will likely be offered a five-year term with a board option to renew. The job comes with an annual salary ranging from $250,000 to $350,000.
Blair faced many challenges during his time on the job, including the mass arrests at the G20 Summit, an investigation involving outgoing Mayor Rob Ford and criticism over the police practice of carding suspects. He also faced very public criticism from Coun. Doug Ford, who had to apologize after alleging that Blair had leaked details of an investigation to the media.
Questions and controversy about police use of force also dominated Blair's term, culminating in the shooting of teenager Sammy Yatim aboard a streetcar in July 2013. The shooting was captured in numerous videos and an officer now faces a second-degree murder charge for his role in the shooting.
"It's a tricky role," said Mukherjee. "I believe chief Blair did it to the best of his capacity and did it honourably."
In addition to a new chief, there will be change on the citizen and council representatives who comprise the seven-member Police Services Board.
The board has one citizen representative appointed by council and three representatives appointed by the province. There is also three elected representatives on the board. These elected reps can include three council members or two councillors and the mayor, who has the option of not sitting on the board. Incoming Mayor John Tory has not yet said whether he will sit on the board.
Coun. Mike Del Grande opted not to seek re-election for his council seat, creating one vacancy. Coun. Michael Thompson was re-elected to his council seat Monday and told CBC News that he will pursue another term on the police board.
It's not known whether Coun. Frances Nunziata, who was also re-elected Monday, will seek reappointment when council selects its board appointees in December.