Serbia is an independent country currently negotiating an EU-memebership. In order to get to Serbia, Russia would have to go through at least one EU-contry or Turkey.
Why do you say that? The negotiations seem to have been progressing since 2011, and Slovenia ratified Serbia's Stabilisation and Association Agreement without delay; they only seemed to have faced opposition from Lithuania.
Historically, Transnistria in USSR was used as military foothold, to capture Moldova, pretending that this is just a conflict or a civil war. Russian Empire/USSR/Russia used that trick many many times. For example, Ukraine was captured by USSR using "Kharkiv People Republic" controlled by Moscow. Today, Russia tries to capture Ukraine again using "Lugansk People Republic" and "Donetsk People Republic".
Transistria is at border of Ukraine and Moldova, owned by both, with roughly equal populations, but both Moldovans and large part of Ukrainians were at same side. For example, leader of separatists was captured by Moldovan police in Ukraine capital city. Why "conflict" happen if both native nations were at same side?
1) its economy is far too screwed up for the EU to include
2) there's still the Kosovo problem, that won't go away soon
3) Croatia and Slovenia will veto an EU membership of Serbia.
It is more than likely that Serbia will turn to Putin instead - and when Putin says "shut them down", Serbia will comply.