The supposed plan has drawn mixed feelings from even the Trump faithful, and was rebuked by Democrats.
News sites such as NBC News and Axios said Mr Trump planned to exit the White House in Marina One, the presidential transport helicopter, and then take a flight on Air Force One to the Florida rally, in a snub to Mr Biden who beat him in the November election.
“The Trump talk could create a split-screen moment: The outgoing president addressing a roaring crowd in an airport hangar, while the incoming leader is sworn in before a socially distanced audience outside the Capitol,” Axios reported on Monday (Dec 7).
Mr Trump, 74, might even announce that he will be running for the 2024 presidential election that day, the reports said.
The UK Daily Mail quoted White House spokesman Judd Deere as saying: “Anonymous sources who claim to know what the President is or is not considering have no idea.
“When President Trump has an announcement about his plans for Jan 20, he will let you know.”
Mr Trump has so far refused to concede his defeat and continue to make baseless claims about massive electoral fraud.
It is rare, but not unprecedented, for a US president to be absent in the swearing-in ceremony of his successor.
NBC News reported that four other president did this, with the last one being Mr Richard Nixon, who departed the White House after his resignation 46 years ago, and did not attend the inauguration of Mr Gerald Ford in 1974.
The news reports say there has been mixed reaction about the Florida rally plan by Mr Trump. US Representative Lois Frankel, a Democrat, was quoted by The Palm Beach Post as saying a countering public event by the outgoing President would be “rude, disrespectful and embarrassing”.
Mr Willie Guardiola, who organises pro-Trump street shows of support throughout Palm Beach County, told the same newspaper: “Why is he planning a rally when he won the election?”
He added: “I can’t relate to another rally. I can’t promote another rally, because we have to do first things first” by continuing the legal challenges in court.