A recent statement basically said that after the Balkans (and by implication in the statement, Turkey) there will be no further EU expansion.
That statement was from Mr Prodi, who is an outgoing EU official, and the comments were it should be taked as exactly that - a statement from a nearly ex-official. The EU (and NATO) has already included 3 former Soviet provinces - Latvia, Estonia, Lithuania. If e.g. Ukraine formally files an application to join and does correspond the requirements satisfied by those three, it will be difficult for the EU to justify why Ukraine cannot be a part of Europe. It is, after all, situated mostly further to the West than e.g. Estonia (never mind Turkey) and a significant chunk of Ukrainian territory was historically a province of the Austrian Empire.
Russia's greatest concern should be not about its neighbours' EU membership - but perhaps about the prospect of its own EU and NATO accession happening in separate bits and pieces
- starting from the Baltic Republic (around Kaliningrad/Koenigsberg), followed by the North-Western Republic with its capital in St.Petersbourg, and so on.
Well, a common border with the EU makes this at least
physically not impossible, which might be what brings unease into some Russian minds.