Donna Shalala, the university's president and former member of Bill Clinton's cabinet, told the club she wanted to join last month, The Miami Herald reported Wednesday.
The request came after a female lawyer's application was rejected.
Club President Adam Lubkin said at a club meeting Monday the organization welcomes Shalala.
"Speaking on behalf of the board, we would be honored to have you as our first female member if you choose to apply," Lubkin told Shalala in an e-mail.
Shalala made her request after receiving a letter from Natalie Lemos about the club's no-female membership policy.
Lemos is a season-ticket holder and the mother of four. One of her sons is a high school football player.
She said she liked the Touchdown Club's primary goal of helping Miami-Dade high school football players who aren't quite good enough to play for Miami or other major football teams to win scholarships at smaller colleges.