Dodik in August was formally ousted by Bosnia’s electoral authorities after he was sentenced to a year in prison and banned from politics for six years.
Slovenian media have reported that Dodik’s family owns a number of properties in the country, including villas at the Adriatic Sea coast.
There were no immediate reports that Dodik has tried to enter Slovenia recently.
The United States played a key role in brokering a peace agreement that ended Bosnia’s 1992-95 bloody ethnic conflict that killed 100,000 people and displaced millions.
Dodik’s policies are widely seen as undermining the tense peace in Bosnia between the country’s three ethnic groups — Bosniaks, who are mainly Muslim, Serbs and Croats.
Russia and neighboring Serbia have supported Dodik in his rejection of the decisions to remove him from office, calling them anti-Serb.
The Dayton peace accords for Bosnia allowed for the creation of the Serb-run and Bosniak-Croat entities, bound by joint central institutions.
There have been fears that Moscow could help stir instability in Bosnia and the Balkans to avert some of the attention from the war in Ukraine.
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