(CNN) -- An abandoned baby whale that has been trying to suckle from yachts in an Australian harbor appeared to be weakening Wednesday as wildlife workers considered ways to save it.

Unless rescue workers can come up with a plan soon, the starving 2-week-old calf might have to be put to death, officials said.

"It's a really sad and difficult situation," said a spokeswoman for the New South Wales Department of Environment and Climate Change (DECC), who spoke on condition of anonymity, as is customary.

"It's caught the heart of Australians, and at the moment the public is really, really desperately wanting something to save the whale."

Humpback whales are in the middle of their annual migration from the Antarctic to tropical waters to breed and then back again.

The calf was first spotted Sunday in waters off Sydney. Officials think it most likely was abandoned by its mother but aren't sure why.

On Monday, it was seen nuzzling up to a moored vessel in an attempt to find milk, the DECC said. Watch the abandoned baby whale »

Wildlife officials towed the boat out to sea, and the calf followed. They had hoped that the baby would link up with a passing group of humpback whales.

But the calf, unable to find its mother or another lactating female willing to be a surrogate, returned to the harbor Tuesday.

On Wednesday, officials tried once again to lure the calf to open waters. But it refused to follow the wildlife officials' boat.

"It obviously feels very secure in the harbor," the spokeswoman said.

An expert from Sydney's Taronga Zoo examined the whale and determined that while it was not suffering undue stress, it was getting weaker due to lack of food.

Now officials are hoping to use an inflatable sling to tow the calf farther out to sea, where it stands a greater chance of being reunited with its mother.

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"Maybe -- just maybe -- we will have some luck," the spokeswoman said. "It is possible -- it might not be probable -- but it's possible that it could be picked up and adopted."

Some Australians have suggested that wildlife officials take the animal into captivity, but that is unlikely to yield results, said Chris McIntosh of the National Parks and Wildlife Services.

"As the calf is still being breast fed, we have no way of feeding or socializing it," McIntosh said in a news release. "So taking this humpback into captivity is not an option."

Calves suckle for 11 months and are "very very attached to their mothers," the spokeswoman said.

"Unless it can go out to open water and find a mother, I don't really know what's going to happen."

All About Sydney (Australia)