Mr Trump has purportedly told advisers his intentions of running for president again next election. News website Axios was the first to report the news, with the New York Times following suit.
Mr Trump is said to have shared his thoughts about the 2024 candidacy with his advisors after pledging he would go to court with “valid and legitimate legal challenges” over electoral fraud allegations.
He said he “will not rest” until there is an “honest vote count” though independent election observers have rejected claims of widespread fraud.
In a statement released last week, Mr Trump said: “We all know why Joe Biden is rushing to falsely pose as the winner, and why his media allies are trying so hard to help him: they don’t want the truth to be exposed.
“The simple fact is this election is far from over.
“Joe Biden has not been certified as the winner of any states, let alone any of the highly contested states headed for mandatory recounts, or states where our campaign has valid and legitimate legal challenges that could determine the ultimate victor.
“In Pennsylvania, for example, our legal observers were not permitted meaningful access to watch the counting process.
“Legal votes decide who is president, not the news media.”
Mr Biden has labelled the president’s refusal to concede defeat “an embarrassment”.
He referred to Mr Trump as the “previous president” and praised the “refreshing” conversation with Mr Biden.
Speaking at Prime Minister’s Questions, he said: “One of the many merits of the excellent conversation I had yesterday with president-elect Joe Biden was that we were strongly agreed on the need for once again the UK and the US to stand together to stick up for our values around the world.
“To stick up for human rights and stick up for global free trade, to stick up for NATO, and to work together in the fight against climate change. It was refreshing, if I may say, to have that conversation and I look forward to many more.”
The Prime Minister conceded he had enjoyed a good relationship with Mr Trump.