As I explained in Do first hand accounts of Genghis Khan exist?, two of three oldest contemporary accounts of the Mongols are written by the Chinese (in wider sense, though), based on the oral account of Daoist Master Chang chun (Qiu Chuji) who had met Genghis Khan in person, or the Chinese (more precisely, Khitan) intellectual who served both Genghis and his son Ögödei, Yelü Chucai (d. 1244).

While the former narrates the memoir of Daoist Master who was asked by Genghis about the immortal elixir, the latter focuses more on the political circumstances and the movement of the Mongols in the last years of Genghis Khan. The rough line of Chucai's account is now also available in interactive app.: https://www.arcgis.com/apps/MapJournal/index.html?appid=e0fe47ae592c4cab8930bbb37ce41269

There seems to also be some 'unofficial' as well as official accounts by Jin (Northern China) authors on the siege, as I mentioned in Is there any Mongolian accounts of dealing with Black Plague?, but I'm not sure whether these details account can date further back into the lifetime of Genghis (The cited part in the linked thread was supposedly occurred in the reign of Ögödei).

On the other hand, I suppose the majority of the accounts on the alleged brutality of the Mongol's expedition in Genghis's last years in Central Asia is roughly based either on the pens of the Islam or the Persian authors. While a few contemporary author belonged to the former milieu, the latter's tradition, Persian chronicle writing, began with Ata-Malik Juvaini (d. 1283 CE) in the 1250s, nearly a generation after Genghis's death.

Reference:

• Hymes, Robert. 'Epilogue: A Hypothesis on the East Asian Beginnings of the Yersinia pestis Polytomy'. In: Pandemic Disease in the Medieval World: Rethinking the Black Death, ed. Monica H. Green, pp. 285-308. Kalamazoo, MI: Arc Medieval Pr., 2014.
• Jackson, Peter. The Mongols and the Islamic World from Conquest to Conversion. New Haven: Yale UP, 2017.