Essentially would anyone in China and/or Japan and/or Europe have knowledge of a landmass East/West of them based on the knowing something was across the (future) Bering Strait by the time Columbus sailed? Would the Mongols or their descendants have talked to the Itelmans, Koryaks, Chukchies, Aluti, Ayni, Ayvens, Kamchadals or any other local tribes and learned from them about it?
I mentioned albeit briefly for a while ago in When did Asia learned about "the discovery of America" and how much did they knew about it? that the trading networks of Ainu people from the 13th to 15th centuries who mainly resided in Hokkaido and Sakhalin did not seem to extent beyond the Northern Kuril Islands.
The Ainu people also had a contact with the Mongolian local government in Lower Amur river, so I suppose [the limitation of] their knowledge on north-easternmost part of Eurasia largely also defined the knowledge of the Mongols (Yuan Dynasty) as well as the Chinese (Ming Dynasty) there. I'd also strongly recommend to check how much of the modern russian far east did the chinese explore?'s answer by /u/_dk