It's not completely impossible, but...nah.
When a country's government decide to invite a foreign prince, they are usually doing so with their future ruler's connections in mind - the idea is that he could use his familiarity with Europe's ruling dynasties to better represent the interests of the country. At this time, the princes of Serbia are connected to...some Romanian and Hungarian nobility, and that's it. A monarch who is personally friendly with the German or Russian court is, in theory, much better than a monarch who is personally friendly with the Hunyadi or Catargiu estates.
Then there's the attitude of great powers. Russia wouldn't want it because the man who sat on the Serbian throne in 1878 was an Austrian stooge. Austria probably wouldn't want it because, stooge or not, they don't want to encourage any ideas of Slavic unity.