Or just not have a united Russia form in the first place.
One of the reasons why Siberia took so long to move into (despite its relative isolation), is that the Steppes are in the way and, honestly, its alot of cold mountains, bogs, and thick forests: not exactly the place that can support large population densities, easily support steppe-type nomads, or make for the first choice of otherwise migrating peoples. Russia went east because it was the open direction and, after Muscovy united the other city-states and bumped up against a powerful Scandinavia, Poland, and Ottoman-backed Crimean Khanate, there wasen't really any better way to expand. Keep Russia fragmented, and I doubt any of its regional principalities are going to focus too much attention east, lest they get taken advantage of in the opening by one of their rivals further West.
But I'd say Crimea or Astrakhan (Or another Volga-based Tartar polity) are your best bet. Persia and China both have the troubles of there just being... alot of wasteland between them between the parts of Siberia that are profitable/productive (Sable fur, early on). Crimea or another southern Tartar nation seem the most likely to be able to modernize and be driven to expand into the raw-resource rich region, due to their connection to the global market via the Ottomans/Black Sea trade.