Shares of Papa John's closed up 7.7% to $44.82 on the news.
Restaurants Brands, which is the parent company of Burger King, Popeye's Louisiana Kitchen and Tim Hortons, could team up with ousted former CEO John Schnatter and investment capital firm 3G Capital to make the purchase, according to DealReporter.
Papa John's management began accepting submitted offers for an acquisition last year, according to a Reuters report in September. The company was thrown into disarray following the ouster of Schnatter, who stepped down in July following reports that he used a racial slur during a conference call.
Schnatter has not gone quietly, however, last year suing the company he founded. Last week, a judge ruled that the company had to hand over corporate records to Schnatter.
Separately, Papa John's announced that it appointed Marvin Boakye as its first chief people officer.
"Boakye's expertise will help us to continue to push Papa John's forward in our transformation to become a better place to work for our 120,000 corporate and franchise team members," said Papa John's President and CEO Steve Ritchie. "In our search for a chief people officer, our goal was to identify a proven talent development leader with expertise in driving organizational change.