After the images, taken during Germany's 1-1 draw with Serbia in Wolfsburg on Wednesday, appeared online, "they presented themselves and confessed they were the three alleged perpetrators", confirmed local police spokesman Thomas Figge.
"They gave a preliminary statement presenting their version of events."
Another supporter, identified by German tabloid Bild as Andre Voigt, a journalist who had gone to the match as a fan, filmed the trio insulting Manchester City players Sane, whose father is from Senegal, and Gündogan, the son of Turkish immigrants.
The German Football Association on Friday condemned the verbal attacks in the "strongest terms" and said it would ban from matches any perpetrators confirmed to have made the chants.
Voigt said the men had chanted "Heil Hitler" and shouted "we need another small Austrian".
"Every time Sane touched the ball, they insulted his colour. Gündogan, was insulted as a Turk. They spoke in pseudo-Turkish accents every time he had the ball. And then they'd start again with 'black, black, black!'"
The men are aged between 30 and 40, said Figge.
Probe to continue
"The police will continue their investigation into incitement to hate and send the file to the prosecutor's office early next week," said the police spokesman.
Gündogan, along with Mesut Özil , was the centre of controversy before the World Cup last year for posing for a photo alongside Turkish President Recep Tayyip Erdogan.
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Meanwhile, midfielder Leon Goretzka said those responsible for the chants must be dealt with accordingly.
"The video shocked me and decisive action has to be taken against it," said the 24-year-old Bayern Munich player.
"We stand for diversity, integration should be a matter of course, I can only call on everyone to act with a lot of courage and put people like that in their place."