The Biden campaign said the questions were only suggestions, and that the hosts were free to ask whatever questions they liked. A spokesman said the campaign would not suggest questions for future interviews.
The incident comes after days of speculation about Mr Biden’s health, which some Democrats believe should force him to stand down from his campaign.
Four senior Democrats privately told colleagues on Sunday they thought Mr Biden should quit the race.
Jerrold Nadler, Adam Smith, Mark Takano and Joseph Morelle, all of whom are ranking members of congressional committees, said the campaign should be suspended, the New York Times reported.
Mr Biden performed poorly in the television debate, and has since claimed he is the “first black woman to serve with a black president”.
On Friday, in an interview with ABC News, he said only the “Lord Almighty” could tell him to end his campaign, and insisted he was sharp enough to continue in the White House after November’s election.
However, some serving White House officials believe that Mr Biden is too old to continue, according to one person speaking to the New York Times. They said he had “steadily shown more signs of his age in recent months”.
Several Democrats have publicly called for Mr Biden to make way for a younger candidate, and a grassroots campaign named “Pass the Torch” has been established to push for that decision.
The Democratic Party cannot change its nominee without Mr Biden’s consent, because he won the primary contest earlier this year virtually unopposed.