Pizza made global headlines in July after Animals Asia started a petition to close the "ocean theme park" at the Grandview Centre in Guangzhou, China.
Videos show the "teary-eyed" bear slumped on the floor of his enclosure.
Neither the Grandview Centre nor the Yorkshire Wildlife Park would comment.
The Yorkshire Wildlife Park houses a specially created habitat for polar bears, which is currently home to four animals.
The park's Project Polar is an "innovative habitat" for polar bears, including a research and conservation programme.
"We would be delighted to see Pizza end up at Yorkshire Wildlife Park," said Animals Asia's welfare director Dave Neale.
"There can be a happy ending - Pizza would not only enjoy incredible facilities, he would also be part of a community of bears."
The charity said no financial payment would be offered for the bear, "with the fear that any funds could be used to buy more animals".
The owners of the indoor zoo in Guangzhou insist they have made improvements to the park since July. But Animals Asia said conditions were still cramped, with "nothing natural".
The "ocean theme park" is also home to beluga whales, walrus calves, a wolf and arctic foxes.