Mr Biden said he is “looking forward to being able to debate him” but “we’re going to have to follow very strict guidelines”.
Mr Trump returned to the White House on Monday after three days of treatment for Covid-19 at the Walter Reed National Military Medical Centre.
Mr Biden told reporters while boarding a plane to Delaware: “I think if he still has Covid, then we shouldn’t have a debate.”
The next debate is scheduled for October 15, with a third due to take place on October 22.
Mr Biden’s campaign says he tested negative for Covid-19 earlier on Tuesday.
Meanwhile, vice president Mike Pence and his Democratic challenger, Kamala Harris, are poised to meet for their own debate that will offer starkly different visions for a country confronting escalating crises.
The face-off in Salt Lake City is the most highly anticipated vice presidential debate in recent memory.
For Ms Harris, the debate is her highest-profile opportunity to vocalise how Mr Biden would stabilise the US, especially when it comes to resolving the pandemic and addressing racial injustice.
She will be able to explain her views on law enforcement, an area in which she is viewed warily by some progressives, given her past as a prosecutor.
Ultimately, the debate is a chance for voters to decide whether Mr Pence or Ms Harris are in a position to step into the presidency at a moment’s notice.
It is hardly a theoretical question as the 74-year-old Mr Trump combats the virus, and Mr Biden, at 77, would become the oldest person to become president if he is elected.
While the debate is likely to cover a range of topics, the virus will be at the forefront.
They will appear on stage 12.25ft apart separated by plexiglass barriers. Anyone in the small audience who refuses to wear a mask will be asked to leave.
The vice president is a 61-year-old former Indiana governor and ex-radio host, an evangelical Christian known for his folksy charm and unwavering loyalty to Mr Trump.
Ms Harris is a 55-year-old California senator, the daughter of a Jamaican father and an Indian mother. She is also a former prosecutor whose pointed questioning of Mr Trump’s appointees and court nominees and cool charm on the campaign trail made her a Democratic star.
She will make history as the first black woman to appear in a vice presidential debate. Democrats hope the historic nature of her candidacy will help energise key groups of likely Democratic voters — African Americans and young people, in particular — who have shown less excitement for Mr Biden.
