The White House has not revealed how many staff members have tested positive since Mr Trump's own diagnosis.
Who else around the president has tested positive?
Press secretary Kayleigh McEnany became the latest high-profile figure close to the president to confirm a positive test earlier on Monday.
US media said two other aides to the press secretary had had a positive result. Ms McEnany was seen speaking to journalists without wearing a mask on Sunday but said no members of the press had been listed as close contacts by the White House medical unit.
First Lady Melania Trump, senior aides and three Republican senators have also tested positive.
President Trump's diagnosis has upended his election campaign, as he faces Democratic challenger Joe Biden on 3 November.