It seems logical that any Chinese explorer could've sailed east around Siberia, through the Bering Sea, and into North America. I am aware that there are plenty of theories about Chinese explorers discovering North America, but from what I could gather from the websites I could find, these seem to be based on scant rather than the wealth of evidence that one might expect to find.
So, this bears the question: What did the Chinese think lied to the North? Why didn't the Chinese just sail north and find the Americas? And if they did, why didn't they do more with that new continent like the Europeans did?
It's a great question and one that demands we look at a few different angles.
Firstly is motivation: For most of China's history, expansion had been to secure borders in the form of extracting tribute1. I am of course generalising here and there were (naturally) some explorative missions as well2, though these were fewer and further between than one might think. China did not have the motivation to investigate the far North of their realm as they already had access to spices, materials and populations in every direction - including the North3. There was simply no great demand.
Secondly, we have to look at the potential benefits vs risks. The Chinese had known that there were people to the North of their lands since at least the the 7th century4 (and probably before that) in the form of the Mongols, Buryats, Teleuts and other 'forest people5' as they were referred to. The land north of Manchuria became poorer, harsher and the people there 'less civilised'6 in Chinese eyes. Thus the potential risks were high and the benefits low.
Thirdly, we have to look at sheer geography. Natural populations grew smaller once past Manchuria mainly due to there not being the resources to supply large populations7. Even today we see a small portion of humanity in the far North compared to elsewhere, and that is even with modern logistics. Another point to make is that the area to explore was **vast**. As late as 1821 parts of Chukotka were still being mapped8. The area in question was so huge and so inhospitable, it's comparable with the Arctic itself.
In conclusion the Chinese lacked the motivation to explore beyond the Mongolian borderlands due to the imbalance between risk and reward combined with more lucrative exploits in other directions. I hope this answered your question, if any moderators feel I have not properly supported my argument, please contact me and I'll be happy to edit.
1: Lee, Ji-Young (2017), China's Hegemony: Four Hundred Years of East Asian Domination, Columbia University Press. Page 18.
2: Wolbert Smidt (2001) *A Chinese in the Nubian and Abyssinian Kingdoms (8th century***, International Journal of Archaeology published online.
3: Lee, *China's Hegemony: Four Hundred Years of East Asian Domination*, Pages 61-65.
4: This is mentioned in Book 30 of the Book of Sui, of which an English-Chinese pdf link is here: Chinese Notes .
5: Again, book of Sui.
6: Jacques Gernet, *A History of Chinese Civilization* Cambridge University Press 1996 P.186-87.
7: Jacques Gernet, *A History of Chinese Civilization* Cambridge University Press 1996 P.12 -15.
8: Benson Bobrick, *East of the Sun* Heinemann publishing 1992 Pages 224-227.