Yorkshire Wildlife Park has asked Guangzhou's Grandview Aquarium to let them move Pizza, as he is known, to their specially designed polar bear habitat.
"The good news now for Grandview is that they now have the chance to put their mistake right," Dave Neale, Animal Welfare Director for Animals Asia, said in a statement.
"Thanks to this incredible offer from Yorkshire Wildlife Park there can be a happy ending and the negative publicity they have suffered can yet be turned into a positive news story. From talking to them I know they know that mistakes have been made in terms of their animal facilities and on-going care."
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Grandview deputy manager Li Chengtang told state media it was "hard to judge the appropriateness of the living space since China doesn't have regulations about such things."
Jason Baker, vice president for PETA Asia, which has also campaigned for Pizza's release, told CNN that "the lack of animal protection laws in China has allowed some of the most deplorable, backwards and decrepit facilities to continue operating."
"Animals are separated from their homes and families and confined to tiny cages and enclosures. Captivity drives many animals insane, causing them to bar bite, self-mutilate and spend hours a day pacing."
A spokesman for Grandview told CNN the aquarium had not received the British zoo's offer.
He added that scientific research and preparation is conducted for all animals to ensure they're comfortable in the aquarium and accused foreign organizations of "hyping up" Pizza's situation.
Yorkshire Wildlife Park's offer is dependent on Grandview agreeing not to replace Pizza with another polar bear or similar-sized animal, it said in a statement. Nor is any payment being offered for the bear himself, due to fears that "any funds could be used to buy new animals."
Animals Asia said that costs of transferring the bear will be raised if the offer is accepted, and that the Park has significant experience moving animals across borders.
CNN's Serenitie Wang contributed reporting from Beijing.