United States media commentary has been underlining that any attempt at self-pardon could either trigger impeachment proceedings against President Trump, or lead to his indictment for federal crimes in courts where the legal validity of the self-pardon would inevitably be put to test.
Mr Trump already has raised questions about his use of the presidential pardon power.
The tweet followed The New York Times' publication of a confidential letter over the weekend, in which Trump's lawyers argued to special counsel Robert Mueller that the president's broad powers mean he could not have obstructed justice.
A spokesman for the special counsel declined to comment on Trump's tweets.
So why did Giuliani say it?
The issue for the midterms is not whether Democrats are scheming to impeach Trump.
While that question has never been tested before the country's highest court, Trump might well become the first sitting USA president to test that theory.
Should Trump try to pardon himself and Congress fail to act, it would set a "dangerous precedent", said Gerhardt, because it would not only dramatically expand the power of President Trump, but every subsequent president. You say he didn't.
Mueller is investigating Russia's efforts to help elect Trump, whose legal team is weighing whether to agree to sit down with the special counsel.
An executive order is a legally-binding directive issued by the president to government officials and agencies which can not be overturned by Congress, according to a report in Sky News. The pardons infuriated the prosecutor, Lawrence Walsh, and the $47 million investigation resulted in only one person sent to prison.
In reality, the FBI began a counterintelligence investigation in July 2016 to determine if Trump campaign associates were coordinating with Russian Federation to tip the election. The only remedy for a president's wrongdoing would be impeachment, he said. "If he shot James Comey, he'd be impeached the next day", he said.
Trump's lawyers don't want him to be interviewed by Mueller, accusing the independent prosecutor, himself a former Federal Bureau of Investigation chief, of trying to "trap" the president in a lie.
"Your office clearly lacks the requisite need to personally interview the president", it said. White House press secretary Sarah Huckabee Sanders later claimed that the president "certainly didn't dictate" it.
On Thursday, Trump stunned much of the political world by announcing a presidential pardon for the conservative commentator Dinesh D'Souza and floating the possibility of pardons for the television personality Martha Stewart and the former Gov. Rod Blagojevich of IL.