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.

The drilling rig was destined for a yard in Turkey to be decommissioned when a towline broke and it ran aground on Lewis.
It is now temporarily anchored in the island's Broad Bay where divers will inspect the structure for damage.
But councillor Angus Campbell has said it could remain longer term.
He has written to the rig's owner, Transocean, to consider breaking up and recycling parts of the structure at facilities near Stornoway on Lewis.
Hugh Shaw, the Secretary of State's representative for maritime salvage and intervention, who is overseeing the salvage operation, has said a decision on the final destination of the rig has still to be made.
In his letter to Transocean, Mr Campbell said: "We are pleased that you continue to engage with the local supply chain and, given the significant and positive economic impact to the islands, would now ask that serious consideration be given to the use of local facilities and engineering expertise in carrying out the necessary repairs.
"As you will be aware, there is an established oil and gas supply chain in the islands with considerable lay down area at the Arnish facility and good connections for skilled workers to move in and out as required.
"Secure additional storage for recyclable parts pending resale could be available at Creed Park on the outskirts of Stornoway.
"We would be very happy to work with Transocean, Smit Salvage and other relevant key stakeholders to ensure that direct and indirect benefits are, as much as possible, retained in the islands."
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.
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The leader of Western Isles local authority, Comhairle nan Eilean Siar, has said the rig Transocean Winner could be scrapped on the islands.