Depends on what you mean by colonizing. You could argue that when the Qing dynasty took control of China in in the 1640s, they brought the dynasty's homeland of Manchuria under Chinese control for the first time since the Yuan dynasty. Manchuria is not quite Siberia, but they were able to project power into the region. The 1689 Treaty of Nerchinsk settled the northeast boundary between China and Russia at the Amur river, the Russians having given up significant land claims made by freebooters in the 1670s. Clearly getting the only other power in Siberia to relinquish land indicates the Chinese held sway in the region.

Qing China, like the previous dynasties, generally did not engage in European style colonization. Many have interpreted this to mean that Qing China was an "insular" nation - far from it! They actively conquered and ruled over non-Chinese peoples like the Uighurs in Turkestan and Tibetans. They also continued to keep small states in Korea and Vietnam in tributary status. The Kangxi emperor did not try for more land in the treaty of nerchinsk because compared to their main foreign concerns in Xinjiang, Korea and southeast asia, poor and sparsely populated Siberia was almost an afterthought.