The humpback whale, nicknamed "Colin" by Australian media, was found at Pittwater after apparently being abandoned by its mother off Australia's east coast.
After U.S.-based whale rescue experts said the animal could not be saved without sophisticated equipment, wildlife authorities said the fast-weakening calf would probably have to be put down unless it could be paired with a migrating whale pod.
"I guess it's fair to say that we're getting close to that position at the moment. We're really, really hopeful that there can be some other possible way through," Environment Department spokesman John Dengate told Australian radio.
The local manager for the New South Wales state national parks service, Chris McIntosh, said Colin had been nuzzling up to a moored vessel in an attempt to find milk, mistaking the yacht for its missing mother.
On Monday a team of workers towed the private yacht out to sea to try to lure the calf into deeper water, hoping that it would find its mother or another passing whale pod, but it was spotted close to the beach at Pittwater again on Tuesday.
McIntosh said while it was distressing, it was natural for some animals to abandon their young.
A decision on whether to put down the whale with a large dose of anesthetic would be made on Thursday, he said. Chances of it surviving past Monday without milk were 100 to one, he added.
Whale calves generally only survived five to seven days without their mothers, McIntosh said. Blood tests were being carried out on Wednesday to determine how fast the whale was weakening.
"Assuming it's separated from its mother from Saturday, we are at about day five," he said.
Whale pods are frequent visitors to Sydney's beaches as they complete their annual migration to the Antarctic and back to breed in warmer waters off Australia's northern coast.
(Reporting by Rob Taylor; editing by Roger Crabb.)