Rodgers was a guest host on "Jeopardy!" this month as the show goes through rotating hosts following the death of Alex Trebek, who died in November following a lengthy battle with stage 4 pancreatic cancer.
During Rodgers' first week as guest host, ratings for the game show spiked 14% from the previous week, according to TV broadcasting site TVNewsCheck.
Rodgers helmed the game show to a first-place finish on the syndication chart for the period ending April 11, with a 5.6 live-plus-same-day national Nielsen rating.
That placed the show ahead of "Family Feud" (5.2 share), and "Wheel of Fortune" (5.1 share). It was the best performance by "Jeopardy!" in a month, according to TVNewsCheck,
The three-time NFL MVP started his stint as the quiz show's guest host on April 5. The bump in ratings came after Rodgers took over for Dr. Mehmet Oz, who hosted the show over the previous two weeks.
"Other than the Super Bowl, this is the honor of a lifetime," Rodgers, 37, said in a Twitter promo for the show.
"Following the footsteps of a legend is something that I know a little bit about," he continued, comparing following Trebek to replacing NFL legend Brett Favre as the Packers' quarterback more than a decade ago.
Ratings will likely be a factor in determining who gets the permanent hosting gig. Rodgers previously said he would absolutely take the job if it was offered to him.
"I would love to be the host of ‘Jeopardy!,’ yes," Rodgers said on "The Pat McAfee Show."
The Super Bowl XLV MVP explained how he would potentially do it, saying he wouldn't "need to give up [playing] football."
"They film 46 days a year. I worked 187 this year in Green Bay," Rodgers said during an interview with The Ringer. "That gives me ... 178 days to do 'Jeopardy!' So I feel like I could fit 46 into that 178 and make it work. It would be a dream job for sure, and I’m not shy at all about saying I want the job. That’s how I went into it. I want an opportunity to be in the mix."
Rodgers had some notable moments during his hosting stint.
Contestant Ken Jennings, whose 74-game winning streak and $2.52 million in earnings are show records, was the first to take over for Trebek, who served as the host for "Jeopardy!" since 1984, presiding over more than 8,000 episodes.
On Wednesday, the producers of the show announced that George Stephanopoulos, Robin Roberts, LeVar Burton, David Faber, and Joe Buck will take turns guest hosting as the search for Trebek's permanent replacement continues.
Fox News' Tyler McCarthy and Jessica Napoli contributed to this report