Gauck told the Kremlin last week that he would not attend the Games, Der Spiegel weekly magazine reported at the weekend.
But a spokeswoman said Gauck’s absence should not be over-analysed, telling Der Spiegel that there was no rule that German presidents always attended the Winter Olympics and
The Russian parliament recently passed a law banning "pro-homosexual propaganda" which provoked international outrage and fears of increased persecution of gays as it was enacted against a background of widespread and officially tolerated homophobia.
Gauck's absence - assumed to be a principled one - has made headlines in Russia. Opposition politician Boris Nemtsov wrote on his Facebook page that it was a “noble act” by the German president.
But head of the Russian parliament's foreign delegation Alexey Pushkov attacked the decision.
"The German president Gauck has not criticized the killing of children and women in Pakistan and Afghanistan. But he is so critical of Russia that he doesn't even want to travel to Sochi,” he wrote on Twitter.
Gauck has been critical of Russia in the past and a meeting between the president and Vladimir Putin was cancelled earlier this year.