The requests broadly ask for any document or email related to a series of highly publicised incidents since Trump became president, including the ouster of National Security Adviser Michael Flynn and firing of Comey, the people said.
The list demonstrates Mueller's focus on key moments and actions by the President and close advisers that could shed light on whether Trump sought to block the FBI investigations of Flynn and of Russian interference.
His team is also eyeing whether the President sought to obstruct the earlier Russia probe overseen by Comey.
The special counsel team's work in recent months has zeroed in on Paul Manafort, a former chairman of the Trump campaign, and Flynn. An official close to the probe said both men are under investigation.
Mueller's agents have questioned witnesses and business associates of both men about whether the men sought to conceal the nature of consulting work they did that could have benefited foreign governments. In a raid of Manafort's home last month, agents sought to seize records related to Manafort's finances.
Over the past few weeks, White House lawyer Ty Cobb has begun sending records to the special counsel. Cobb is working within the White House to gather more of those documents and has told staffers and other lawyers that he hoped to turn over many more this week.
Cobb declined to discuss the subjects that Mueller's team has questioned him about.
Mueller also asked for any email or document the White House holds that relates to Manafort, the people briefed on the requests said. Manafort resigned from the campaign before the election amid scrutiny of his work for a powerful Ukrainian political party aligned with the Russian Government.
Mueller has requested that the White House turn over all internal communications and documents related to the FBI interview of Flynn in January, days after he took office, as well as any document that discusses Flynn's conversations with then-Russian Ambassador Sergey Kislyak in December.
Mueller has also asked for records about meetings then-Deputy Attorney General Sally Yates held with White House counsel Don McGahn in late January to alert him to Justice Department concerns about Flynn, as well as all documents related to Flynn's subsequent ouster by the White House.
Regarding Comey, Mueller has asked for all documents related to meetings between Trump and Comey while Comey served at the FBI, records of any discussions regarding Comey's firing and any documents related to a statement by then-press secretary Sean Spicer made on the night Comey was fired.
He has also asked for any documents related to a meeting Trump held in the Oval Office with Russian Foreign Minister Sergei Lavrov the day after Comey was fired.
Mueller has also asked for all records related to the June 2016 meeting at Trump Tower with a Russian lawyer hosted by the President's son, as well as all documents related to the White House's response to the publication of accounts of that meeting in July 2017.
Mueller is moving as quickly as he can and is taking his mandate very seriously, one government official told the Washington Post. He believes for the moment that he has all the resources he needs and that the office is now a fully formed agency vigorously using a grand jury for subpoenas and interviews, the official said.
"I am convinced that no matter where they end up, this investigation will run to completion even if they fire Mueller," the official said.
"There is a feeling of inevitability now that we didn't have before - not of the outcome of the investigation but that there will be an outcome. There is no escaping this thing, whatever the conclusions."
