"I have to find that we're going to be treated fairly, because everybody sees it now, and it is a pure witch hunt", Trump added, while incorrectly saying that Mueller, a Republican former Federal Bureau of Investigation director, has a "group of investigators that are all Democrats". Trump and he had discussed disclosing Trump's repaying Cohen, and "he was well aware that at some point when I saw the opportunity, I was going to get this over with", Giuliani added.
In his place, Trump tapped Republican defense attorney Emmet Flood, who brings experience wrangling with investigators when he represented President Bill Clinton during House proceedings to impeach him.
It was not immediately clear in what context the possibility of a subpoena was raised or how serious Mueller's prosecutors were about the move.
How Trump led the USA to the brink of a trade war
But in recent months, he has voiced strong support for Trump's tougher trade approach to China and steel and aluminum tariffs . Beijing has been backing up its towering ambitions in the semiconductor sector with money and tax breaks.
The questions cover a series of matters that Mueller has delved into during his investigation, which in May will have been underway for a year, although some of them were focused on Trump's decisions and actions that could be deemed obstruction of justice.
Giuliani in an appearance on Fox News on Wednesday had said Trump fired James Comey as FBI director past year because Comey declined to state publicly that Trump was not at the time a target of the agency's investigation into Russia's role in the election. Because everybody sees it now, and it is a pure witch-hunt.
The questions also involve key moments from the early months of the Trump administration, including his reaction to Attorney General Jeff Sessions' recusal from the Russian Federation investigation and Trump's firing of his national security adviser, Michael Flynn.
Even if Mueller's team chose to subpoena Trump as part of the investigation, he could still fight it in court or refuse to answer questions by invoking his Fifth Amendment protection from self-incrimination.
"If you fight back because you people say something wrong, or they leak like they've been doing, if you fight back they say, oh, that's obstruction of justice", Trump said. He did not mention that Mueller himself is a Republican.
Mueller has already floated the idea of issuing a subpoena against Trump that would compel him to appear before a grand jury if he will not speak to investigators, and former New York City Mayor Rudy Giuliani has speculated that there is a 50-50 chance that will happen.