Salihamidžić's father Ahmed and mother Šefika gave him the nickname "Braco", meaning "little brother" in Bosnian, since Hasan has an older sister, hence his current nickname "Brazzo". He finished elementary school and played in the local club. Then, Salihamidžić moved to Velež Mostar where he stayed until 1992. That year, Salihamidžić was called up to the Yugoslavia under-16 team, for a match against the CIS under-16 team in Belgrade. Days after the match, Bosnian Serb troops began a siege on the Bosnian capital Sarajevo, forcing his father to look for opportunities in Western Europe for his son.