Koepka carded 69 for the second straight round Friday. He became the first defending champion to break 70 in his first two rounds of the U.S. Open since Scott Simpson accomplished the feat 31 years ago.
Kopeka told reporters he feels great despite still trailing Rose for first place.
"I've got a chance," Koepka said. "That's all you can ask for. I just need to make a few putts. Sometimes the hole just needs to open up."
Koepka is no stranger to having a chance. With a victory, Koepka would join Scotland's Willie Anderson (1903-05) as the only player to win three straight U.S. Opens.
Koepka also won the PGA Championship in Bethpage, N.Y., last month.
"If I can get off to a good start tomorrow, have that feeling where the hole's opening it up, it could be a fun round," Koepka said.