A drop in tourist arrivals and a glut of available rooms have produced price cuts at Hong Kong's hotels. And with the number of rooms expected to rise by about a third, to nearly 37,000, in the next three years and the Chinese takeover of the colony in 1997 likely to put a damper on tourism, the bargains seem set for a long stay.

But travelers have to do some homework to get the best prices. The Hong Kong Hotel Association (telephone 369-9577) has a referral service that lists official room rates, but because of fears of a price war the service does not say which hotels are offering discounts.The effort involved in searching out discounts can be well worth the trouble. The luxury Conrad Hotel, which opened recently and is aiming to compete with such Hong Kong legends as the Mandarin and the Peninsula, is offering discounts of 40 percent on its posted rates until the end of April. That means a standard room that normally goes for $192 can be had for about $115.

The hotel had a dismal January room occupancy rate of 14 percent.

The neighboring Marriott, meanwhile, is offering a summer package (from May 26 to Sept. 14) at $286 for two nights, compared with a posted rate of $224 a night. The Grand Hyatt, part of a gleaming new complex on the waterfront, offers a similar package from March 1 to the end of August. Rooms are offered for $147 a night, sharply down from its normal rate of around $218.

The best prices are probably to be found a few notches below the super-luxury class, according to a travel agent, Frank Lee of Sampan Tours.

Hotels such as the Marco Polo, the Sheraton, the Royal Pacific Tower and Ramada, he points out, all currently offer rooms for between $80 to $110.