A lost baby whale which captured Australians' hearts as it tried to suckle from a yacht it thought could be its mother will soon be killed to end its suffering, wildlife rangers said Thursday.

"He's taken a really serious turn for the worse just now," said John Dengate, spokesman for the Department of National Parks and Wildlife which has been at the forefront of efforts to save the animal.

"The vets have had a look, they've said he's having breathing difficulties, his flippers are at an unusual angle, he's not going to last much longer, you should put him down," he told national radio.

The baby humpback was discovered on Monday in Pittwater bay near Sydney's Palm Beach, trying to suckle on the hull of a whale-sized anchored yacht, after apparently being abandoned by its mother.

In a remarkable effort to return it to the ocean, the calf -- dubbed Colin after the man who first found it -- was lured out to sea by the 'mother ship'.

But after failing to find its own mother or an adoptive parent among the pods of whales passing Pittwater, Colin returned to the bay and again began trying to suckle yachts.

With public concern over the calf's fate growing, the army was asked whether it could help with a flotation device to take Colin back out to sea and a scientist suggested it could be fed formula milk through an artificial teat.

But the logistics of feeding and looking after a whale calf which would need about 230 litres of milk a day were insurmountable, experts said.

"The vets who had a look at him were really surprised at how fast he'd gone downhill," Dengate said.

"Their advice to us was 'he's not going to last much longer, he's suffering and you should take action'."

"It's a really tragic result from an operation that people worked really, really hard (on)."

Nobody knows why the uninjured calf was apparently abandoned by its mother, with some experts saying that, while this happened sometimes in the wild, it was also possible the two had become separated somehow.

The humpbacks are on the return leg of a remarkable annual round trip from the Antarctic to tropical waters to breed, and they can be seen ploughing homewards not far off Sydney's beaches on most days.