An enormous great white shark - believed to be one of the biggest on record - has been spotted off the coast of Hawaii by divers who took a swim with the predator.

The six-metre female shark - bearing similar markings to "Deep Blue," the largest great white shark recorded - made its surprise appearance on Tuesday, joining other sharks feasting on the carcass of a sperm whale off Oahu.

"We saw a few (tiger sharks) and then she came up and all the other sharks split, and she started brushing up against the boat," said Ocean Ramsey, one of the divers, recounting the extraordinary encounter to the Honolulu Star Adviser.

"She was just this big beautiful gentle giant wanting to use our boat as a scratching post," added Ramsey, who swam with the shark all day and captured stunning pictures. "We went out at sunrise, and she stayed with us pretty much throughout the day."

Ramsey said the animal, believed to be at least 50 years old and weighing an estimated 2.5 tonnes, was "shockingly wide", at approximately 2.4 metres across, and may be pregnant.

Deep Blue, who has her own Twitter account and was the subject of a documentary several years ago, had previously been spotted around Guadalupe Island off Mexico.

Ramsey studies sharks, advocates for their conservation and leads cage-free shark diving tours. She and her team observe and identify sharks and share that data with state and federal partners.

Hawaii waters are usually too warm for great whites compared with California's Pacific coast, where they feed on sea lions and elephant seals, Ramsey said, suggesting that the giant white might have headed to Hawaii because of hunger and a need for extra nutrients in pregnancy.

The Hawaii Department of Land and Natural Resources said in a statement on Wednesday that the decomposing whale carcass that had attracted so many sharks had drifted to about 13km south of Pearl Harbor after being towed 24km offshore days earlier.

The department said tiger sharks have been "almost continuously" feeding on the whale and said it was aware of photos of the great white.

The agency's Division of Conservation and Resources Enforcement Chief Jason Redull cautioned people to stay out of the water around the dead whale.

"We don't want anyone to get hurt if a shark swimming around the carcass mistakes them as food. Understandably, some people want to get into the water either out of fascination or to get photographs, but it is truly dangerous to be around this carcass with so much shark activity," he said.

Sharks usually only bite when they're curious or mistake people for their natural prey but are unpredictable, Ramsey said.

"Big pregnant females (sharks) are actually the safest ones to be with - the biggest, oldest ones - because they've seen it all, including us," Ramsey said. "That's why I kind of call her, like, a grandma shark."

The natural resources department said there are reports people climbed on top of the whale carcass and removed its teeth, which may be a violation of state and federal laws.

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Officials said the carcass it is currently drifting away from shore, but a predicted shift in the winds could once again push it back towards Oahu.