President Trump has asked Michael Flynn, his former national security adviser, about the prospect during a White House meeting on Friday according to The New York Times. It follows a TV appearance by Mr Flynn last week in which he floated the idea.
Appearing on right-wing news outlet Newsmax, Mr Flynn suggested the president should impose martial law and deploy the military to “rerun” the election.
“At one point in the meeting on Friday, Mr. Trump asked about that idea,” The New York Times wrote, citing White House insiders.
Mr Trump responded to reports of the meeting on Twitter, writing: “Martial law = Fake News. Just more knowingly bad reporting!”
He has also called for a rally in Washington DC on January 6 to coincide with both houses of Congress meeting to formally confirm Joe Biden’s election.
Tweeting about it, he claimed: “Statistically impossible to have lost the 2020 Election. Big protest in D.C. on January 6th. Be there, will be wild!”
Mr Flynn was pardoned by Mr Trump after pleading guilty to lying to the FBI during its investigation into Russian election interference in 2016.
He told Newsmax: “Within the swing states, if he wanted to, he could take military capabilities and he could place them in those states and basically re-run an election in those states.
“It’s not unprecedented.
READ MORE: Donald Trump lashes out at UK’s new Tier 4 lockdown measures
The Democrat defeated his Republican rival in November after projections showed he had passed the threshold of 270 Electoral College votes needed to win.
California, the most populous state, delivered its 55 electoral votes to Mr Biden last Monday – officially confirming his victory.
Speaking in Delaware afterwards, he said: “The rule of law, our constitution and the will of the people prevailed.
“Our democracy – pushed, tested, threatened – proved to be resilient, true and strong.”
He is to be sworn in as president on January 20.
Outgoing US President Mr Trump has also retweeted the UK’s plans to introduce a new Tier 4 lockdown.
With it, he claimed lockdowns are “worse than the problem itself” alongside news of the Prime Minister’s announcement.
He tweeted: “We don’t want to have lockdowns.
“The cure cannot be worse than the problem itself!”
Mr Trump has also hit out at other European countries for announcing fresh lockdowns to combat the virus.
He said: “What the hell are they [Europe] doing?
“I think I’ll go over and explain it to them.”