At a news conference, Muhammad Syaugi of Indonesia's National Search and Rescue Agency said the identification process was proceeding as quickly as possible, but said it was unlikely the remains of all passengers would be found.
The accident has resurrected concerns about Indonesia's patchy air safety record which led to a now-lifted ban on its planes entering United States and European airspace.
The spokesperson for Indonesia's search and rescue agency, Yusuf Latif, has not confirmed the discovery of the black box.
He has said he's certain it won't take long to locate the hull of the aircraft and its flight recorders due to the relatively shallow 30 meter (100 foot) depth of the waters where it crashed.
Prior to the accident, the first for a 737 Max 8, the plane on a previous flight had experienced problems with the sensors used to calculate altitude and air speed, according to a spokesman.
We will remind, in the company of Lion Air Group said that Boeing had previously been technical problems that appeared during the flight from Bali to Jakarta.
The airline gave no reason for the personnel change but said in a news release it was made at "the instruction and the decision of the (Indonesian) transportation ministry".
The plane's black boxes, as the cockpit voice recorder and flight data recorder are known, should help explain why the almost-new jet went down minutes after take-off.
After about 30 minutes of passengers waiting on the tarmac, they were told to board again while an engine was checked.
The search had been previously hampered by a strong undercurrent.
The pilots landed the Airbus SE A330 safely after obtaining groundspeed information from air traffic control and using the jet's radar altimeter, according to a preliminary report from the Australian Transport Safety Bureau.
He added that the quickest way to identify bodies found in the wreckage is to match the DNA of victims with that of their relatives, and said that the police have since contacted family members and requested they fly into Jakarta to aid in the process.
Tjahjanto said a team will be deployed to the identified location to confirm the findings.
A Lion Air passenger jet of the Boeing 737 MAX 8 series at Jakarta Airport.
Boeing experts were expected to arrive in Indonesia on Wednesday and Lion Air has said an "intense" internal investigation is under way in addition to the probe by safety regulators.
Lion Air said the jet had only gone into service in August.
This crash is now more deadly than the AirAsia crash in December 2014, when 162 people were killed.
A ban on Indonesia aircraft was imposed by the European Union and the United States in 2007 as a result of "unaddressed safety concerns". The FAA lifted the ban in 2016 after the country's airlines showed signs of improvement. It has been expanding aggressively in Southeast Asia, a fast- growing region of more than 600 million people.