“The visit is still on but we will be reviewing the situation closely,” The Star said, quoting an official from the British High Commission in Kuala Lumpur.
The royal couple are in Kuching as part of their week-long visit to Malaysia.
This is their first visit to Malaysia.
Heavy rain has resulted in nearly 2,000 people evacuated from homes.
Many roads in George Town were submerged in water.
The military has mobilised its forces and assets to join volunteers in flood relief work.
After visiting Singapore and Malaysia, the royal couple will next visit India.
Prince Charles, 69, is the heir apparent to the British throne as the eldest child of Queen Elizabeth II.
Prince Charles, Camilla arrive in Malaysia for official visit