Fritz eased past Swiss qualifier Dominic Stricker 7-6(2), 6-4, 6-4, on Sunday to secure his place in the last eight in New York, where he is bidding to become the first American man to win a Grand Slam singles title in two decades.
"He's gotten me seven times," Fritz said of the Serb, who beat Borno Gojo in straight sets to reach the quarters.
"There's no one on tour that has any kind of a record like that against me, so I'm hoping one of these times I've got to get him. The US Open quarters would be a pretty good time."
Fritz, one of three US men in the last eight, was thrashed 6-0, 6-4, by Djokovic in the Cincinnati quarter-finals last month but he said he would take positives from that defeat.
"It's good that I got the one in Cincinnati out of the way," said Fritz. "Not that it would have necessarily changed anything, but I was not at my best that day.
"I'm glad for that, because I think I'll be in a much better head space approaching this match... I have nothing to lose.
"I'm not going to overplay. I'm not going to do anything different because I'm playing Novak. I'm going to play my game, play within myself and trust that if I play well, it's enough."
