Thompson is 21 under with his 62 in Saturday's third round giving him a two-stroke lead from Eric Cole, who posted 64 with a strong late-round stretch, and England's Aaron Rai, who shot 66.
Australia's Jason Day is tied 30th at 11-under after posting a five-under 66 which included an eagle and two bogeys.
Thompson leads going to the final round in two years on the PGA Tour for the first time.
"There is a lot of losers every week out here," he said.
"You can have great weeks and finish top 10. At the end of the day your goal is to win the golf tournament."
Thompson, who had bogey-free rounds on Thursday and Saturday, might have to maintain the torrid pace at TPC Deere Run where low scores are the norm - his 62 matched the lowest round of his career.
"It was just my day. Hit a lot of good shots on the back nine and finished the round off well."
The 25-year-old is a former University of Georgia golfer who tied for second place last week at the Rocket Mortgage Classic and shared ninth place in the U.S. Open.
Fellow American Cole's back nine included four birdies and an eagle as he also bids for a first title on the PGA Tour.
Hayden Springer, who had an opening-round 59, was back in the groove after a challenging second round, carding 66 to share fourth place at 17 under with Taiwan's CT Pan (68).
Jordan Spieth (63), the tournament's 2013 and 2015 winner, had the second-best score Saturday before sitting in a tie for 12th place at 14 under.
"It was just a good solid round," Spieth said.
"If I can be as solid as I was (Saturday) and maybe catch a couple extra breaks, it would take something extremely flawless to have a chance."
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