No nation is going to take **all** of Siberia, for the reason stated in my comment. However, that said, the notion of another nation taking some chunk of Siberia has been around for centuries, dating to at least the Khanate.
More recently, at least Japan (as witness their concept of the ''Northern Resource Area'' before and during WW II, and the trade component of casus belli for the Russo-Japanese war of 40 years earlier) and China (lumber and minerals were routinely taken from Siberia during the Ming and Qing ('Manchu') dynasties) have had designs on Siberia.
England had what we might nowadays call a ''look-see'' at the proposition when she was involved in the Opium Wars, but cooler heads prevailed, fortunately. In the 1890s, even the U.S. Senate toyed with the notion of extending the Seward purchase into Asian Russia (the czars were always needing money for their assorted multi-front wars), and had McKinley not been assassinated, the U.S. might very well have ended up owning a piece of Siberia.
Likely the most obvious candidate today would be China, and I should suppose such an action on their part would NOT be a matter of simple greed or expansionism. We don't get the chance to observe just how unstable the PRC is. It's quite easy to design an historical ''what-if'' game wherein China, in an attempt to rally national unity due to desperation of solving its internal problems, might concoct a ''war'' out of thin air wherein the object would be the taking of some portion of Siberia. Is this likely in the absolute sense today, or in 5 years' time? No. In 50 years' time, however, all bets are off; tell me how relatively stable both Russia and China are, as unisoverign nations, and I'll give you a guesstimate of the possible sequel. The probability at that time, possibly even a decade or so sooner, will be well above zero.
Geopolitical weakness has ALWAYS bred opportunism, in any period you like of mankind's history. Until/unless Russia can become something resembling a modern coherent nation, it will continuously be a target of such opportunism, whether military or economic (you can ask Soros about this latter point, to name just one example).
China is not going to swipe a significant and valuable part of Siberia from Russia. Period. It would be suicide and both sides know it.
Now THAT position would have been strategically indefensible. We would have held Vladivostok with our sea power and the Russians would have held or retaken everything else because of their land power.