"Katie, she tested very good for a long period of time and then all of a sudden today she tested positive," Trump said. "She hasn't come into contact with me, she spent some time with the Vice President. It's I believe the press person."
US media outlets confirmed Trump was referring to Katie Miller, who recently married White House senior adviser Stephen Miller.
Trump said Pence has tested negative for COVID-19 following the recent development.
A White House press pool report said, citing a senior US administration official, that six staffers removed from Air Force 2 earlier today ahead of Pence's trip to Iowa tested negative for the virus.
White House Chief of Staff Mark Meadows said they may place additional safety measures in terms of who comes into contact with Trump and Pence. Meadows noted that they have placed additional protocols in the White House over the last two days to make sure Trump and his immediate staff are better protected from the disease.
On Thursday, media reported that a US service member who works as one of Trump's personal valets tested positive for COVID-19.
The United States has about 1.2 million confirmed cases of COVID-19 and more than 75,700 deaths caused by the disease as of Friday morning, according to data compiled by the Johns Hopkins University Coronavirus Resource Center.