Russia never made any official attempt to claim back any land from any of the Soviet Republics as or after they became independent, even in areas dominated by Russophones, such as Narva in Estonia, Transdniestr in Moldova, or Donetsk in the Ukraine.

What they did do was encourage the creation of super-autonomous areas in these regions, with varying success levels. The attempted autonomous area in Narva as D.O.A, while the one Transdniestr succeeded in setting up an independent (although not internationally recognised) state. This also happened in areas containing minorities that were not ethnically Russian but were historically pro-Russian (such as Ossetia and Abkhazia in Georgia).

I've heard that Russian nationalist groups often advocate Russia annexing some such areas, notably the Crimea, which is mostly Russian, already has considerable autonomy within Ukraine, and is home to major Russian military assets such as the Black Sea fleet. The Russian government, though, has never made any concrete or even symbolic moves in this direction.

Source: The politics of security in modern Russia, Mark Galeoti

Also I believe Lara Ryazanova is about to publish a book on the subject of Russians in the 'near abroad'.