If another zoo ends up getting giant pandas, it'll be a "dark horse" zoo with the capital and space to house giant pandas. Something like Zoo Atlanta or Memphis Zoo, where they already have a well-rounded collection, but pandas would seal the deal.
For example, Columbus Zoo planned for giant pandas while constructing their Asia Quest precinct but ended up using that space for sun bears (and now sloth bears). Similarly, Oakland Zoo built an exhibit for giant pandas before that fell through, with that space utilized (quite wisely) by their ever-growing troop of Hamadryas baboons. Omaha's Henry Doorly Zoo almost got pandas (with the site eventually being utilized for the new giraffe herd rooms in African Grasslands) before that deal fell through at the last minute.
We can also rule out any WCS zoo getting giant pandas, given their expense; as Jim Breheny stated in an article a long while ago, "Building and maintenance of a panda exhibit would be an on-going effort that would require tens of millions of dollars up front and annual support monies for pandas for however long they would be in NY… Any agreement to exhibit pandas would have to come with a guarantee of provision for the necessary funds."
The secondary issue with building a giant panda exhibit is you're really building two exhibits for the price of one (or even three in National's case), with a yard for the male, a yard for the female, and two indoor spaces for each. Adelaide's a good example as far as a distillation of that concept, as shown here:
https://www.researchgate.net/public...-plan-of-the-Giant-Panda-exhibit-redesign.png
Theoretically, Disney's Animal Kingdom *could* get pandas, seeing as they have the capital and the parent company has ties with the Chinese government - the issue is where they'd be placed. Columbus is another option as far as having the space within Asia Quest (you could honestly replace the current set of tiger cages across from the main Amur tiger exhibit with giant pandas or construct a giant panda exhibit across from the red pandas, though realistically, that may just become even more space for their Asian elephant herd.
Like I said, I'd see a dark horse zoo getting giant pandas more than anything after San Diego and National.