Jelic, a businessman and economist, was a regional minister of economy and industry in the previous government.
The constitution is unclear about who may succeed Jelic, said Tanja Topic, a political analyst, on Sunday.
Topic said candidates for the vacant post could include Dragan Cavic, the former Bosnian Serb president and a member of the Serb Democratic Party.
Cevic received the second-highest number of votes after Jelic, in October's presidential election.
Candidates could also include Jelic's deputies - Davor Cordas, a Bosnian Croat, or Adil Osmanovic, a Muslim Bosniak.