Born in Munich, Leitner started his football career at FC Unterföhring, joining them at the age of two.
As a six-year-old, he moved to 1860 Munich.

Leitner made his professional debut for his childhood club 1860 Munich on 14 August 2010, coming on as a substitute for Aleksandar Ignjovski in a DFB-Pokal match against SC Verl, setting up an equaliser for Stefan Aigner.
By the end of 2010, Leitner had made eighteen appearances in all competitions.
Prior to his departure in January, his form dipped and he was often relegated to the substitute bench.
Born in Munich, Leitner started his football career at FC Unterföhring, joining them at the age of two. As a six-year-old, he moved to 1860 Munich.
Leitner made his professional debut for his childhood club 1860 Munich on 14 August 2010, coming on as a substitute for Aleksandar Ignjovski in a DFB-Pokal match against SC Verl, setting up an equaliser for Stefan Aigner. By the end of 2010, Leitner had made eighteen appearances in all competitions. Prior to his departure in January, his form dipped and he was often relegated to the substitute bench.
Moritz Leitner