Mr Trump also defended Rudy Giuliani, who he recently hired to represent him in the matter.
Trump again called the special counsel investigation into whether his campaign colluded with Russian Federation to interfere in the 2016 elections a "witch hunt" and suggested that is why his attorneys have advised him against sitting down for an interview. Disputes over legal strategy reportedly led to Dowd's resignation.
It was not immediately clear in what context the possibility of a subpoena was raised or how serious Mueller's prosecutors were about such a move.
The list of four dozen questions, which covered a range of topics, including Russian meddling in the USA election and whether Trump tried to obstruct justice to protect his former National Security Adviser Michael Flynn, was published by the New York Times earlier this week.
Trump lashed out against the investigation in a familiar fashion Wednesday, saying on Twitter: "There was no Collusion (it is a Hoax) and there is no Obstruction of Justice (that is a setup & trap)". "But you have a group of investigators that are all Democrats".
Watch a clip of the president's comments above via CNN.
Even if Mueller's team chose to subpoena Trump as part of the investigation, the president could still fight it in court or refuse to answer questions by invoking his Fifth Amendment protection from self-incrimination.
Giuliani did not consult every member of Trump's legal team before he spoke with Fox News, the New York Times reports. One of Trump's lawyers announced Giuliani's addition to the team on April 19. The list also included questions around former FBI Director James Comey's firing, as well as questions about Attorney General Jeff Sessions. Trump initially said he was eager to be interviewed, but his perspective on Mueller soured a raid last month targeting his personal lawyer, Michael Cohen, in a separate investigation. They have not yet made a decision about an interview. "I would love to speak.Nobody wants to speak more than me.I would love to speak because we've done nothing wrong." he said responding to a shouter question from reporters.
Trump said people's conception of obstruction of justice was "nonsense" meant to stop him from fighting back.
"No questions on Collusion". Some touch on Russian meddling and whether the Trump campaign coordinated in any way with the Kremlin.
Shakeups to Trump's legal team and a leak of potential questions that Mueller might ask the President have created further uncertainty over whether Trump will cooperate.