Murray, who ranks fourth in the nation in passing efficiency, should break former Georgia star David Greene's SEC record of 11,528 yards passing this week. Murray is 99 yards away from matching Greene's total from 2001-04.
Murray is also on the verge of breaking Florida standout Danny Wuerffel's SEC mark of 114 career touchdown passes. Murray has 106.
"It's crazy to think about," Murray said. "I've never been a guy who's worried about stats. It's all about winning, winning, winning, but it's definitely an honor to be alongside some of those guys like Greene and Wuerffel, guys who did some unbelievable things."
Murray threw four touchdown passes in a 44-41 victory over LSU last week after running back Todd Gurley left with a sprained left ankle in the first half.
"I thought Aaron played good during the game," coach Mark Richt said Tuesday. "When the game was over, I thought he had played good. Then I watched the film and I thought he played great."
Georgia (3-1, 2-0 Southeastern Conference) has averaged 41.2 points per game against a tough early schedule that included three top-10 teams, and Murray's senior leadership has been especially important.
"I think he has stepped up his game, even more so than in the past," tight end Arthur Lynch said. "It's not just about who we've played but about his decision making, his ability to make the big play when we need it most, and third-down throws that are pretty vital."
The Associated Press contributed to this report.