Sources said that much-travelled Stojanovic had already agreed to join Levski on a one-year contract with an option to extend for a further year.
Stojanovic led Domzale to the Slovenian league title in 2007 and 2008 and Red Star Belgrade to the Serbian league title in 2014. He also coached clubs in Belgium, China and Latvia and worked as the United Arab Emirates' assistant coach between 2009 and 2011.
The 48-year-old will replace Italian Delio Rossi, who was released following an early European exit last week.
The Blues, as Levski are known in the Black Sea state, were knocked out by Liechtenstein's FC Vaduz in the Europa League's first qualifying round on away goals after the sides drew 3-3 on aggregate on Tuesday.
(Reporting by Angel Krasimirov; editing by Amlan Chakraborty)
