The Serbian centre-back was frozen out of the squad following the fight with teammate Heung-Min Son, and is currently training with the Under-23 side.
As a foreign player he is not allowed to play competitive games for the youth teams, which is making his situation even more difficult.
The player admits he regrets his actions and has offered apology to coach Thorsten Fink.
“I want to apologize specifically to him. I’m really very sorry,” Rajkovic said in an interview with Hamburger Morgenpost.
The player then revealed that he had opted against leaving the club in the summer despite a number of proposals from abroad.
“This is exactly the point: I did not want (to leave). That had nothing to do with the fact that there were no offers. There were clubs (interested) from Holland, Russia and Spain.”
The 23-year-old, who began his career with OFK Beograd, has made 16 Bundesliga appearances for Hamburger SV last season, scoring one goal in the process.