A close adviser to Donald Trump who frequently travels with the US president has tested positive for the coronavirus.

Hope Hicks, a former White House communications director who returned to the administration as a counsellor to Trump this year, travelled to and from this week's presidential debate in Cleveland, Ohio with him.

She was also aboard the president's helicopter, Marine One, for a trip to Joint Base Andrews on Thursday. And she was aboard Air Force One for Trump's visit to Minnesota, where he held a political rally.

Bloomberg News correspondent Jennifer Jacobs, who was first to report that Hicks had contracted the virus, said the senior aide was experiencing symptoms, and had been in close proximity to Trump without a mask in recent days.

Jacobs stressed there was no indication that Trump had been infected.

"The president takes the health and safety of himself and everyone who works in support of him and the American people very seriously," White House spokesman Judd Deere said.

"White House Operations collaborates with the physician to the president and the White House Military Office to ensure all plans and procedures incorporate current CDC guidance and best practices for limiting Covid-19 exposure to the greatest extent possible, both on complex and when the President is travelling."