The 24-year-old has made just four appearances in all competitions for the Bluebirds since joining from Maribor in 2012.
Cardiff's owner, Tan, completed a takeover of the Bosnian side in December, with Velikonja set to be the first player to move between the two clubs.
Sarajevo's director of sport, Abdullah Ibrakovic, told Dnenvi Avaz: "Cardiff's manager Ole Gunnar Solskjaer gave the green light for a loan, just like the player's agent.
"Now the ball is on the striker's side. If he does come, he will be a great replacement for our best striker Nikola Komazec who just left us."