The first televised presidential debate took place in 1960 between Richard Nixon and John F Kennedy.
Since 1987, they have been organised by the Commission on Presidential Debates, which is sponsored by both parties.
But for the first time in nearly four decades, the commission will play no part, leaving it up to the campaigns to reach an agreement.
If ABC goes ahead with the broadcast without Trump, there is the prospect of an empty chair at the debate.
“He can say he won’t do the ABC debate, the optics of pulling out of that debate looks terrible,” Christopher Galdieri, an associate professor of politics at Saint Anselm College, New Hampshire, told The Telegraph.
“Is he scared of her? If he doesn’t show up, ABC can’t send out a posse of reports to drag him there.
“It’s possible Harris could show up and he doesn’t. It’s never happened before.”