University President Neeli Bendapudi announced change for Papa John's Cardinal Stadium on Friday, as the pizza chain said it is removing Schnatter's image from its marketing.
Schnatter admitted to using a racial slur during a May conference call following a Forbes report. McConnell, an avid Louisville football fan, said "there's no place for racism in this country".
But "if I could take it off?"
Fallout has already included Major League Baseball indefinitely suspending a promotion with Papa John's that offered people discounts at the pizza chain after a player hit a grand slam.
Schnatter had previously resigned from the university's board of trustees.
During the call, he reportedly said "Colonel Sanders called blacks n--" and never faced backlash.
Asked whether she was daring the company to sue over the name change, Bendapudi said, "It's not that type of situation at all".
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While Papa John's was once ubiquitous with the sports world, it's partnerships have fallen off over the past few months due to Schnatter's actions.
Mr Schnatter quit as chief executive previous year after criticising the NFL over players' national anthem protests.
In a statement released by Louisville, Kentucky-based Papa John's, Schnatter said Wednesday that the reports attributing use of "inappropriate and hurtful" language to him were true.
"Mr. Schnatter's comments were offensive and inexcusable", the club said in a statement provided to The Times.
Schnatter had used the slur during a media training exercise in May, Forbes reported this week. The University of Louisville said it will remove the Papa John's name from its football stadium, and that it will rename the John H. Schnatter Center for Free Enterprise at its business college. Netflix said Jonathan Friedland used the word in a meeting of public relations staff about sensitive words.
Friedland, who is white, later repeated the word with human resources staff trying to address the original incident, Netflix said. His image and voiceover do appear at the end of two of the top five TV commercials that have aired nationally so far this year according to iSpot.
Papa John's International Inc. began operations in 1984 and had more than 5,200 locations globally. In addition, Schnatter will keep his shares in the company and remain the largest shareholder with 30 percent of the pizza chain's stock.