Zoos in the United States have told China they cannot afford to keep paying $1 million (£580,000) each year for the loan of Giant Pandas.
Zoos say they want to pay China less for renting the animals
The endangered mammals are the A-list celebrities of the animal kingdom when it comes to pulling in the crowds.
Yet zoos in Washington, San Diego, Atlanta and Memphis say current loan deals are not viable in the long-term.
Officials recently made a joint trip to China to say they want to renegotiate fees when current contracts expire.
'Crowds peak and tail off'
Giant pandas are an endangered species, with about 1,600 living in the wild.
For the four zoos that keep them in the US they are a both a top visitor attraction and important case studies for zoological researchers.
Yet the institutions say the cost of keeping the animals is not offset by profits from visitors and merchandising - which peak with the birth of cubs but quickly tail off.
Smithsonian's National Zoo spokesman John Gibbons told the BBC: "There is a possibility that there may be a day when there may not be Giant Pandas at the zoo.
"We have had informal discussions with the Chinese and told them that we can't sustain the current expenditure and we are waiting for a response."
The zoo was the birthplace of "panda diplomacy" in the 1970s when the Chinese Government donated two pandas amid efforts to improve Sino-US relations.
China still views pandas as valuable ambassadors of friendship between the two countries.
In 2000, WNZ signed a 10-year, $10m deal to bring pandas Tian Tian and Mei Xiang to Washington.
The pair had a cub, Tai Shan, last July - for which the zoo paid China a one off fee of $600,000 ($348,000).
San Diego Zoo has paid out even more, because it has had three panda births since 1999.