President Donald Trump's closest aides were not wearing masks when they prepped him in the days ahead of his debate with Democratic rival Joe Biden, one of them said Friday, while the president's family refused to wear masks during the televised event.

"No one was wearing masks in the room when we were prepping the president," said former New Jersey governor Chris Christie, after news broke that Trump had tested positive for the virus.

A big concern now is how many people in Trump's inner circle might also have Covid-19.

Christie said there were "about five or six people" in the room helping the president practice for his first debate this week with Biden ahead of the November 3 election.

Christie, who said he was awaiting the results of his own test, made regular visits to the White House "from Saturday afternoon through lunchtime on Tuesday," joining the team which included former New York mayor Rudy Giuliani, who is now Trump's personal lawyer.

He said he had not noticed the president exhibiting any symptoms of the disease during that time, and neither did Hope Hicks, the aide whose positive test preceded the diagnosis of the president and his wife Melania.

"Hope seemed completely fine, as did the president" he said. 

Trump, 74, and his 77-year-old rival Biden, faced off on the podium in Cleveland Tuesday night. Neither man wore a mask but they stood socially distanced at lecterns on the stage. 

Moderator Chris Wallace of Fox News sat a distance, also without a mask.

In the debate hall, the president's family arrived wearing masks but subsequently removed them, Wallace said.

"Everybody that was in that hall had tested negative," Wallace said Friday.

But he said doctors at the Cleveland Clinic, who were in charge of testing, had ordered everyone except for the candidates and the moderator to wear masks in the hall.

The city of Cleveland announced Friday it was aware of 11 cases of coronavirus "stemming from pre-debate planning and set-up," with the majority of those affected coming from out of state.

"Mrs Trump came in wearing a mask, but took it off when she sat down," Wallace said.

"All the other members of the first family that I saw there, including Ivanka, Tiffany, when they sat down, they weren't wearing masks," he noted.

Wallace said that Biden's wife Jill kept hers on for the 90-minute debate, during which the president mocked his rival for always wearing protective face covering when on the campaign trail.

She kept her mask on when the debate ended and she went up to embrace the former vice president. Melania Trump climbed to the stage without hers on to stand next to the president.