Mr Giuliani added Mr Trump "has no intention of pardoning himself", but the USA constitution, which gives a president the authority to issue pardons, "doesn't say he can't".
In his tweet, Trump again called the investigation a "never ending Witch Hunt" and said it is being led by "13 very Angry and Conflicted Democrats".
Trump doesn't give any legal basis for his claims and suddenly seems to be firing off absurd tweets about the investigation, the way he does about everything else.
"I'm not a lawyer, so I have no idea whether it's legal for Trump to pardon himself or not", Peterson said in a statement provided to the Herald. Those pardons have raised questions about how the president will treat those ensnared in Special Counsel Robert Mueller's investigation into the 2016 election, including - potentially - himself.
Speaking to CNN's Chris Cuomo, Giuliani said that Sekulow and White House press secretary Sarah Huckabee Sanders (who also publicly denied the president dictated the statement) had simply gotten facts wrong about Trump's involvement.
Mr Trump also said he was considering pardoning lifestyle maven Martha Stewart and commuting the prison sentence of former IL governor Rod Blagojevich, convicted of corruption charges.
Later in the same program, former Gov. Chris Christie, R-N.J., dismissed the argument put forward by the Trump legal team that the president inherently can not obstruct justice.
Regardless, other presidents have resisted even considering using the pardon power for themselves.
Clinton's Justice Department didn't conduct an additional review of the president's ability to pardon himself, according to a former senior administration official familiar with the matter.
Bob Goodlatte (R-Va.) mentioned that there's "a prevailing opinion that a President of the United States can exercise the power of pardon on himself".
Still, he stood by the remark about hypothetically shooting the former Federal Bureau of Investigation director as an example of his belief in the strength of the President's immunity.
"The appointment of the Special [counsel] is totally UNCONSTITUTIONAL!"
In a Timesop-ed, former deputy assistant attorney general Harry Litman said the memo's "understanding of presidential power is radical and absolutist". "We are a society based on the rule of law, not of men". House Majority Leader Kevin McCarthy, a Republican from California, told CNN's Dana Bash on "State of the Union" that he doesn't think the President should grant himself a pardon.
No president has ever pardoned themselves. The foundation of America is that no person is above the law. I know this one: "It's because if you bring the grain over the river first, the fox will collude with the Russians to get the chicken".