It seems that China, Republic of Korea (maybe even North Korea), and Mongolia may be interested in transnational natural world heritage sites based on discussions at the World Heritage Convention, including side events.

Side event held at the WHC, jointly organized and hosted by UNESCO, Korea and China:

"Migratory Bird Journeys Across Borders: Conservation of Yellow Sea Tidal Flats through Transnational Cooperation within the East Asia-Australasian Flyway'

Migratory Birds Know No Borders

'The tidal flats and coastal wetlands extending along the coasts of South Korea, North Korea, and China form a single interconnected ecosystem.'

"The committee's vision involves a transnational inscription encompassing the Yellow Sea's tidal flats, including those of China and North Korea, to protect an important habitat along the East Asian-Australasian Flyway for migratory birds." - Joongang Daily Report

Another potential transnational candidate? There are some recently published articles that highlight talks between Korea and Mongolia related to Cretaceous Dinosaur Fossil Sites in Mongolia and Korea.

Preparing for Joint World Heritage Listing of Korean Dinosaur Footprints and Mongolian Bone Fossils (Additional Source)

Current Tentative List:
- Cretaceous Dinosaur Fossil Sites in Mongolian Gobi
- Cretaceous Dinosaur Coast in Korea

*Note: China also has a significant Mesozoic (Cretaceous) Fossil Site in Northeast Asia, which in its comparative analysis is favorably compared to fossil sites found in the Mongolian Gobi

Heo Min, head of the National Heritage Administration, stated, "I proposed to Mongolia that we jointly register Korea's dinosaur footprint fossils and Mongolia's dinosaur bone fossils as a UNESCO World Heritage Site."

Could Mongolia, Korea, and perhaps China collaborate on a broad Mesozoic (or Cretaceous) Fossil Nomination?

I think a transnational one for fossil sites would be more likely. The migratory bird sites are certainly linked but is it worth the effort to keep evolving them into a new transnational site? Seems like a brand new one would be more worthwhile and the Gobi Desert fossils are world renowned.