The US president made the request on an unannounced visit to the hospital outside Washington D.C. in November 2019, blocking both doctors and non-medical staff from discussing his care, NBC News reported.
At least two physicians were said to have refused to sign the agreements, and were not permitted to treat the then 73-year-old, four sources familiar with the matter told NBC News this week.
He returned to the same facility last Friday following his coronavirus diagnosis, and was discharged on Monday.
It is not known whether Mr Trump made the same request for staff NDAs during his weekend admission to the hospital.
Sources familiar with the 2019 visit told CNN he was unlikely to have undergone a routine medical examination, in contradiction with White House statements on the matter.
Mr Trump’s reported NDA request at Walter Reed also came despite protections under the Health Insurance Portability and Accountability Act, prohibiting the disclosure of patient information.
Those laws also apply to the president, whose NDA requests raise questions about why they were deemed necessary before staff could treat him last year.
In a statement to NBC, White House deputy press secretary Judd Deere declined to comment on the NDAs, and said: "Any physician caring for the president is bound by patient physician confidentiality guaranteed under HIPAA,”
He added: “I'm not going to comment on internal procedures beyond that".
Anyone assigned to the president and vice president’s medical team is also required to have special security clearance in addition to abiding by patient privacy laws, NBC reported.
The revelation comes amid concerns that Sean Conley, the president’s physician, has dodged questions on the 74-year-old’s condition in recent days.
He said on Wednesday that Mr Trump continued to show “no symptoms” but would not say whether he had returned a negative test, signing off with a statement reading: "I release the following information with the permission of President Donald J Trump."
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