Emergency agencies who have been conducting the search said their effort has not yielded any fruit.
The General Manager of the Lagos State Emergency Management Agency (LASEMA), Adesina Tiamiyu, told Channels Television that officials would continue with the search until the body was found.
Mr Tiamiyu said the search operation lasted till late night, adding that more boats were deployed on Monday morning while the search continued.
He hinted that the operation was extended to a wider range, saying tidal waves might have moved the drowned body from where the incident took place.
The LASEMA boss, who said they have also alerted those in the neighbourhood to watch out for any floating body, noted that it was not certain if the body would be recovered on Monday.
Until his death, Dr. Orji works at the Mount Sinai Hospital in Surulere area of Lagos State, southwest Nigeria.
He was said to be on his way to Victoria Island for a meeting with the Medical and Dental Association of Nigeria when the incident happened.
Temporary reports from Police authorities revealed that the deceased had asked his driver to stop the vehicle before jumping across the bridge and into the water.
LASEMA also said there was a distress call of a man who parked his grey coloured Nissan SUV at about 4:50 pm around Adekunle and jumped into the Lagos lagoon.
The agency said the vehicle and the driver had been taken to Adeniji Adele Police Station for further investigation.