With just three holes left in the rain-hit second round at Oak Hill Country Club, Simpson was seven under for the day and on track to join 23 other players who have fired 63s in golf's elite championships.
However, the 2012 US Open winner stumbled on his 16th hole, the seventh, when he hit a tree with his approach on the way to a bogey five and had to settle for a six-under-par 64, which equalled the course record.
"I was certainly thinking about it, once I birdied six," Simpson said.
"I was thinking about the all-time Major record, and I was about 99 percent sure it was 63. It's so hard, because on one hand, you want to go for it. You want go for the record.
"But you can't do that on a golf course this hard and I wasn't doing that at any point today. I was trying to be patient and trying to be conservative."
Simpson did not say a single word to his experienced caddie, Paul Tesori, about a possible 62 as they negotiated their last three holes on a rainy day at Oak Hill.
"I knew he was thinking about it," said Simpson, after posting a four-under tally of 136 to sit three strokes off the early lead held by Masters champion Adam Scott.
"I didn't want to talk about it because I thought it would be the wrong thing to focus on coming in. This game is so funny, when you try to make birdies, it seems like you don't.
"It was there (the thought of a 62). It's like the elephant in the room; I knew he was thinking about it. I haven't even talked to him, but I'm sure he was too."
Simpson, who clinched his maiden Major title at last year's U.S. Open, covered his last nine holes in three-under 32 to remain in contention for a first US Tour win this season.
He was especially pleased to cap a gutsy fightback at Oak Hill, having been struggling at five over after eight holes in Thursday's opening round.
"It was a pretty low moment for me," said Simpson, who has recorded four top-10s in 19 starts, his best finish a play-off loss to Graeme McDowell at the RBC Heritage in April.
"But I kind of had a pep talk with myself on the seventh green, and just told myself, 'One hole at a time.' I tried to get a birdie here, a birdie there, and somehow played the last 10 or 11 holes under par.
"I birdied 18 yesterday, which was huge for my confidence and two over felt like 64 yesterday after being five over, so I am extremely happy with my game today."
Simpson sank a series of clutch putts on Friday, including a 35-footer to birdie the par-four fifth, to maintain his surge up the leaderboard.
"All around, it was really solid," said the 28-year-old. "I made some great putts, and made some good par putts to kind of keep the momentum going.
"You know, it's a special feeling to have tied the course record here at Oak Hill."
Twenty-three players have combined to shoot 25 63s in the Majors, American Steve Stricker the most recent to do so in the opening round of the 2011 US PGA Championship.
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- Oak Hill Country Club