Well theres the problems of massively smaller populations than Russia or China, the threat of attack from either of the former, the very different economic factors and techniques to make Siberia useful, all make it pretty unlikely.
As too Samarkind ruling Moscow, controlling Siberia really gives a state very little power. It was useful to Russia as a source of furs, a way to reach the far east, and a nice protected space to the east, but Russia power always came from the Volga valley. A central asian or Iranian polity is going to have to find power from somewhere other than Siberia.
Finally theres always the problem with successful central Asian states - Northern India is just too sweet and easily accessible prize to divert resources to Siberia.