The silk road from the Far East to Asia probably operated from about 200 B.C.E although it was not a direct trading route but worked in stages; so there was no direct contact from say China to Palestine. Marco Polo arrived in China around 1265 C.E. Chazal ascribe Noah's sons as founders of the Greeks etc. There is no reference to Chinese, Koreans or Japanese - so which son takes the honours?
Torah Meira - page 297 says that according to some Magog the son of Yefes is connected with Eretz Sin - ארץ סין. Although there are other translations of ארץ סין - one of the translations is China. This would indicate - at least according to this translation - that the Chinese are descendants of Yefes.
See all about the destinations of some of the 70 nations in Talmud Yerushalmi Megilla (Artscroll edition 12a,3). They quote R. Aharon Marcus in Kessess Hasofer who holds that the descendants of Magog (descendant of Yefes) may be identified with the Mongols, who lived near China (but who are known to have ranged as far as the Danube River). He notes that Arab writers have referred to the Great Wall of China as the "wall of Magog."
Well the Zohar Vayishlach 178a makes reference to the "Royal Tusser" which was also the Greek name for the Chinese domesticated silk worm(as opposed to the wild variety which is also mentioned in the Zohar). So it would appear that the Chinese were indeed known.
Considering that China is made up seven main people groups, it would really depend on which specific people group you are talking about. However, if we take the primary people group, the Han Chinese, who are believed to have emigrated north from India, then according to the Table given in the Jewish Encyclopedia based on the various midrashim, they would have been descended from Ham.
Now from a more Arheological perspective, I give you this:
Heth is the father of the Hittite nation. The Hittites were once regarded by archaeologists as a biblical blunder. Archaeologists said the Bible was absolutely wrong when it mentioned the Hittites, for there was no such people. But since that time, Hittite relics have been discovered in abundance, and scholars are now well aware of the great civilization that flourished under the Hittites. The Hebrew form of this word, Hittite, is Khettai and from this comes the word Cathay, which many of you will recognize as an ancient name for China. Certain of the Hittites migrated eastward and settled in China. Also, another name in this list, the Sinites, is linked with China. It derives from a presumed son of Canaan whose name was Sin. The Sinites migrated eastward until they came into Western China, where they founded the ancient Empire of China and gave their name to the land. There is a direct connection between the word China and the word Sinim, the biblical name for China. (I remember reading as a boy of the Sino-Japanese War, showing how the ancient name still persists.) They pushed eastward and toward the north over the land bridge into Alaska. The Sinites are the people who settled the Americas in prehistoric days and became the ancestors of the Eskimos and Indians who, to this very day, betray their Mongoloid ancestry.
By Stedman in his book The Beginnings.
So I'm going to go with Ham. Though there is also possibility that at least some of the people groups in China were descendents of Avraham Avinu's sons that he sent east(see Ibn Ezra Beresehit 26:1, and Genesis Rabba 65).
Rabbi Philip Biberfeld in Universal Jewish History, writes:
The Sinites. A passage of the prophet Isaiah shows that they are obviously the Chinese. Their land is referred to as far away from Palestine, neither to the north nor to the west. It is highly significant in this connection that the Egyptian reliefs picture one type of Hittites with high cheek bones, oblique eyes, wearing pigtails like the people of Mongolia and China. Comparative archaeological investigations, moreover, have demonstrated with increasing clearness that nearly all basic elements of Chinese civilization have penetrated from the west. Some elements of their early art and industry appear to have come from Mesopotamia and Turkestan. The Biblical name Sin obviously is identical with that of the ancient Chinese province of Chin or Tsin, which conquered all the other provinces, established a unified empire, and gave to China the name by which it is known to nearly all the world except itself. (pg. 90-91)
Rabbi Biberfeld therefore identifies the Chinese as the Sinites, descendants of Cham through Canaan.
On the Mongols:
Magog was the forefather of the Mongols. The designations, 'Mandshu' and 'Mongol', are derived from their original name, 'Magog'. (pg. 84)