"Everybody seems to be in pretty good shape … I think it's changing."
US health authorities in August extended the Covid-19 public health emergency, which began in January 2020.
It will be reviewed in mid-October.
More than one million Americans have died with the coronavirus disease over the course of the pandemic.
Data from Johns Hopkins University shows more than 400 people in the US a day are still dying with the virus, with 2991 deaths reported in the last week.
Others appear to share Biden's optimism, albeit to a lesser extent.
On Wednesday last week, World Health Organisation director-general Tedros Adhanom Ghebreyesus said the world may be nearing the end of the pandemic.
"Last week, the number of weekly reported deaths from Covid-19 was the lowest since March 2020," Dr Ghebreyesus said.
"We have never been in a better position to end the pandemic – we're not there yet, but the end is in sight."
As well as the bold call on the pandemic, Biden issued forceful warnings to China and Russia and expressed optimism over the US economic rebound during the rare interview with 60 Minutes.
Biden, who turns 80 in November, told interviewer Scott Pelley that re-election was his "intention" but the President stopped short of officially confirming he'll run again.