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.
The questions - at least four dozen in all - also show Mr Mueller wants to find out what Mr Trump knew about connections between members of his presidential campaign and Russian Federation.
In January, President Trump told reporters he was interested in talking with Mueller under oath, but behind the scenes, the president's lawyers have been carefully negotiating the terms of those possible talks, CBS reported.
She said later that Flood would be joining the White House staff to "represent the president and the administration against the Russian Federation witch hunt". Instead, Mueller's team agreed to give Trump's attorneys more details on the topics prosecutors wanted to discuss with the president.
In March, Mr Mueller warned during a meeting with Mr Trump's lawyers that he could issue a subpoena for the President to appear before a grand jury, according to four people familiar with the encounter.
During independent counsel Kenneth Starr's investigation of President Bill Clinton related to Monica Lewinsky, prosecutors eventually subpoenaed the president for grand jury testimony.
In 1974, in United States v. Nixon, the Justices unanimously directed President Richard Nixon to comply with a criminal trial subpoena for the White House tapes.
The Times said it obtained the list from someone outside Trump's legal team.
At about 9:30 on Wednesday, Trump tweeted again, quoting a former U.S. attorney who says such questions are an intrusion into the Constitutional powers of the president to fire anyone.
It's the latest shake-up for a legal team grappling with unresolved questions on how to protect the president from legal and political jeopardy in Mueller's Russian Federation probe, which is nearing its one-year anniversary.
"There was no Collusion (it is a Hoax) and there is no Obstruction of Justice (that is a setup & trap)", Trump tweeted.
Trump's lawyers are careful to say that the President hasn't shut the door to a possible agreement for an interview.
While Mueller had a team of more than a dozen seasoned prosecutors at the prime of their careers, Trump's team was led by Dowd, who had decades of experience with large-scale investigations but was in solo practice and nearing retirement.
The leaking of a version of Mueller's potential questions for the President, first published by The New York Times, and the President's reaction on Twitter underscore where the issue is moving, sources say.
The questions reflected what the defence lawyers anticipated Trump would be asked, rather than verbatim queries that Mueller's team provided, the person said. Manafort is now facing a litany of charges under Mueller's investigation. His view of Mueller soured further after raids last month that targeted one of his personal lawyers, Michael Cohen, in a separate investigation.
"What efforts were made to reach out to Mr Flynn about seeking immunity or possible pardon?" goes another.
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