The Welshman shot 4-under-par 65 in the third round to thrill an enthusiastic home crowd. His total through 54 holes is 10-under 197, tying him with the 22-year-old Kaymer, who also shot a 65.
"I feel like I'm driving the ball well, which is key for my game," said Dredge, who came into the tournament as the highest-ranked Welshman in the world at No. 66, but knows he is hardly a favorite.
He will try Sunday to match Ireland's Padraig Harrington as the only players this season to win in their home countries. Harrington beat Dredge in a playoff two weeks ago to become the first Irishman in 25 years to win that event.
Second-round leader Mads Vibe-Hastrup (68) of Denmark is tied for third place with South Africa's Richard Sterne (64) at 9-under 198.