On Twitter, the president said that he and his wife are awaiting their test results and that, "in the meantime, we will begin our quarantine process", just over one month out from the November 3 presidential election.
Trump later tweeted that he and the first lady will begin isolating until they receive their results.
"Whether we quarantine or whether we have it, I don't know", Trump, 74, told Hannity.
Hicks accompanied Trump aboard Air Force One to and from the first presidential debate on Tuesday.
U.S. media, citing unnamed sources, said Hicks was isolated on the journey back from Minnesota after showing mild symptoms and tested positive Thursday morning.
Multiple White House staffers have tested positive for the virus, including Katie Miller, Vice President Mike Pence's press secretary, national security adviser Robert O'Brien, and one of the president's personal valets.
With 33 days left until the election, on Thursday night the President claimed that he and Melania tested positive for COVID-19. Hicks had tested positive, saying: "I just went for a test and we'll see what happens".
Close Trump adviser Hope Hicks tests positive for coronavirus, sources say
Hope Hicks , who serves as counselor to the president, became the latest Trump aide to come down with the highly contagious virus. Treasurys are rallying after the president's positive COVID-19 test. "Then I just went out with a test".
"She tested positive, so whether we quarantine or whether we have it".
Stay tuned to Pinkvilla for more updates.
She went on to become his White House communications director - replacing the controversial Anthony Scaramucci - until 2018, when she moved to California to become an executive at Fox Corporation. After Hicks was diagnosed, Trump tweeted that he and Melania were waiting on test results. And it stands as the most serious known public health scare encountered by any sitting American president in recent history.
Trump plans to continue carrying out his duties but is expected to remain home for two weeks, canceling campaign events as doctors watch him at the White House.
According to an administration official, speaking anonymously to the Associated Press, she was quarantined away from others on the plane. Public health professionals say mask-wearing is key to helping to prevent the virus from spreading.
Meanwhile his Democratic opponent, former Vice President Joseph R. Biden has mostly done events and fund-raisers virtually, prompting regular ridicule from Mr.
She was also with him on the Marine One helicopter Wednesday when he flew back to the White House after a rally in Minnesota.
Mr Trump has sought to diminish the significance of the virus amid surveys showing a majority of Americans disapprove of his handling of the pandemic, which he has said would simply "disappear".
White House deputy chief of staff Dan Scavino, counselor to the president Hope Hicks and senior policy adviser Stephen Miller walk across the South Lawn before departing the White House late last month.