Tendentious articles on that topic have a long history: During the Russo-Japanese war both sides (represented by Shōgorō Tsuboi and Dmitriy Anuchin) would claim kinship between the Koreans/Japanese and the Paleosiberian peoples; the Russians were attempting thusly to belittle the Japanese (as mere Paleosiberians) and the Japanese were attempting to lay claims on the land currently occupied by Russians (and rightfully belonging to their Paleosiberian bretheren).
Now, what is the current state of science? Well, the Paleosibirian languages are not related closely to one another, but there is a theory about certain words (a "substratum") being common to all peoples of the Pacific North, including the Koreans and the Japanese. It was proposed by the Finno-Ugric languages expert Valeriy Nikolayevitch Chernetsov. Common cultural fads have been addressed on and again as well: the expert on Paleosiberian peoples Chuner Taksami has penned an article on "the common elements in the cultures of the Pacific North" in 2009. It cites the extant articles comparing ornaments and temporary shacks used by whalers, fishermen, seal hunters; or on similarities in their shamanism. Research in this direction is, at least, a thing.
Moving further to the West makes giving a reply more difficult due to the difficulty of drawing a natural border between Siberia and China before the Russians had arrived in the seventeenth century. There are peoples which traditionally lived on both sides of the current border and throughout modern history the Chinese were interested in the pelts and in the ivory (along with European goods) provided by the Russians, who had, in turn, an interest in silk, ceramics, tea and the other goods from Asia (see the Kyakhta trade). Of course this would involve the Paleosiberian peoples as well (since they were the ones who provided the pelts and the ivory).