"I do not know who this girl is", Cainsaid at a press conference at Arizona he predicted to quell the controversy.
Herman, a cancer survivor, fought hard, but the family said it knew the time would come when God would carry him home.
Cain had survived Stage 4 cancer roughly 14 years ago, but that history made him part of a high risk group for COVID-19, the respiratory illness caused by the virus.
As recently as Monday, an update on Cain's website said he was still being treated with oxygen, but his organs were "strong". Trump campaign spokesperson Tim Murtaugh told CNN at the time that Cain did not meet with Trump at the Tulsa rally.
Trumptweeteda statement Thursday afternoon calling Cain a "special man, an American Patriot, and great friend".
Cain had entered an Atlanta-area hospital for treatment on July 1.
Cain, 74, had been hospitalized since early July after he began having trouble breathing. "And yet we also felt real concern about the fact that he never quite seemed to get to the point where the doctors could advance him to the recovery phase", Calabrese said. He dropped out of the race aftersexual harassment allegations surfaced.
Cain was a staunch Republcian and ran for president in 2012.
Cain was on the board of the Federal Reserve Bank of Kansas City and served as CEO of the National Restaurant Association.
Mr Cain, who had hoped to become the first black man to win the Republican nomination, was initially considered a long-shot candidate. I just got off the phone with his awesome wife Gloria, daughter, Melanie, and son Vincent to express my deepest condolences to the entire family.