The US president proposed the stunt during his stay at Walter Reed Medical Center, according to The New York Times.
Mr Trump is said to have suggested he initially appear frail upon leaving the hospital, before dramatically opening his button-down shirt to reveal a Superman t-shirt beneath.
The move was meant to be a “symbol of strength”, according to the newspaper, but it was eventually dropped.
The report emerged as Mr Trump made his first public appearance since returning to the White House.
The maskless president spoke from a White House balcony on Saturday at an event called “a peaceful protest for law & order,” attended by a few hundred people standing on the lawn below.
“I’m feeling great,” he said, before declaring the pandemic which has killed more than 210,000 Americans was “disappearing”.
His appearance was seen as a first step towards resuming full campaigning next week.
Meanwhile his physician Dr Sean Conley has said the president is no longer at risk of transmitting coronavirus.
Dr Conley said Mr Trump meets the Centers for Disease Control and Prevention (CDC) criteria for safely leaving self-isolation.
However some medical experts have expressed concerns that he could be declared free of the risk of transmitting the virus so early in the course of his illness.
Just 10 days since an initial diagnosis of infection, there is no way to know for certain that someone is no longer contagious, they said.
Dr Albert Ko, an infectious disease specialist and department chairman at the Yale School of Public Health, said the White House appeared to be following CDC guidelines for when it is appropriate to end isolation after mild to moderate cases of Covid-19.
But he warned that those who have had severe cases of the diseases should isolate for 20 days, noting Mr Trump was treated with the steroid dexamethasone, which is normally reserved for patients with severe Covid.