The suspects, who took 29-year-old Queenie Rosita Law from her home, freed her after family members paid a reported HK$28 million (USD 3.61 million).
They had initially demanded up to HK$50 million for the release of Law, the granddaughter of late textiles tycoon, Law Ting-pong.
Footage from Cable TV showed uniformed officers descending on a village in the eastern part of the city in the early hours of Thursday, while hundreds of heavily armed officers have also been searching Ma On Shan Country Park since Tuesday, the South China Morning Post said.
She said she could not give details about the case as police investigations were ongoing.
Roadblocks have been set up and helicopters and marine vessels were deployed in the city-wide manhunt, which began after Law was released.
"The investigations for the case is ongoing," a police spokeswoman told AFP Thursday.
She said the search operation was taking place "(all) over the territory", without giving further detail.
"Arresting them is just a matter of time," an unnamed police source told the SCMP.
But a series of high-profile kidnapping cases shocked the city in the 1990s.
The eldest son of the city's richest man Li Ka-shing was kidnapped in 1996 by the infamous crime boss Cheung Tze-keung, nicknamed "Big Spender", who also kidnapped property tycoon Walter Kwok in 1997.
Cheung fled to China but was later arrested by mainland authorities and was executed in 1998.