Gauck, 76, is expected to explain his decision in a meeting with German Chancellor Angela Merkel on Monday, the newspaper reported. Gauck’s term ends in March 2017.
A spokeswoman for the president declined to comment.
The German president holds a largely ceremonial role, represents the country in matters of international law and at official gatherings.
The president is not directly elected by the people, but rather by a committee, the Federal Convention, which consists of members of the German parliament and the same number of delegates sent from the state parliaments.
The president has a term of five years and can only be re-elected once. Any German citizen over the age of 40 is able to become president. (Courtesy Reuters)