A picture of the 22-year-old kneeling just before the start of the warm-up in Prague went viral on Twitter with many on social media assuming it was in support of American football players protesting racial inequality.
Trump said he wants players who kneel during the US national anthem to be fired.
"I'm doing that before most matches just to remember, you know, the two most important people that have passed away," said world number 20 Kyrgios in reference to his late grandmother and grandfather.
And, prompted whether it had anything to do with the Trump protest, he offered a puzzled look: "Fuck, no.