The cub will be the first giant panda to be born in Hong Kong.
Earlier this year, 10-year-old Ying Ying mated naturally and was also artificially inseminated.
However, the staff at Ocean Park are unsure which method has resulted in the successful pregnancy.
Ying Ying was sent to mainland China's Sichuan province this spring to take part in a breeding programme.
The 100kg female - described by the park as "inquisitive, active and vigilant" - attempted to mate naturally with two male pandas on five different occasions and one of the attempts was deemed successful.
But to improve the chances of a viable pregnancy, Ying Ying was also artificially inseminated.
Repeated ultrasound scans in late September confirmed she was carrying a foetus, Ocean Park officials said.
Two panda maternity specialists have travelled to Hong Kong from Sichuan to provide pre- and post-natal support and the park's executive director of zoological operations Suzanne Gendron said she was "cautiously optimistic" about the birth.
Panda reproduction is a notoriously difficult process, with females only ovulating once a year.
It is common for giant pandas to re-absorb the foetus into the womb in the late stages of pregnancy.
The gestation period is typically five months and one or two cubs are usually born.
A giant panda in Hong Kong called Ying Ying is pregnant and due to give birth within a week, officials at an amusement park say.