On Tuesday, former White House chief strategist Steve Bannon is expected to meet with the panel, while Trump's former campaign manager, Corey Lewandowski, is expected to testify this week before the committee as well.
It was the first time Mueller is known to have used a subpoena against a member of Trump's inner circle, the Times said.
Rep. Mike Conaway, the Texas Republican leading the House Intelligence Committee Russia investigation, declined to comment on a subpoena or Bannon's testimony as he went back into the committee's secure spaces.
U.S. intelligence agencies, including the CIA and NSA, concluded with "high confidence" in 2016 that Russian Federation was behind an effort to thumb the scale of the USA election for Mr Trump.
Mr Bannon's attorney was not immediately available for comment. His work has previously appeared in the American Prospect Online, and he blogs frequently at Sadly, No!
Trump disavowed Bannon, saying his former top aide had "lost his mind", and later nicknamed him "Sloppy Steve".
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Called White House Rasputin, he was sacked last August after eight months of controversy with or members of Trump's team, but things were twisteded completely two weeks ago, when, with publication of book Fire and Fury, y went out to Light some incendiary statements of Bannon, in which it crossed eldest son, Donald Trump Junior, of "traitor". Bannon was soon ousted as the executive chairman of the hard-right website Breitbart News.
Fox News also reported that Bannon had been subpoenaed.
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Mr Bannon was present for several controversial moments in the Trump administration, including the firing of former national security adviser Michael Flynn after he misled the Vice President about his dealings with Russian Federation. He continued to speak with President Trump and tried to promote the president's agenda.
The House Intelligence Committee is speeding toward a conclusion of its interviews in its Russian Federation investigation.
He and Trump's son-in-law have never seen eye to eye; their White House feuds were a poorly kept secret, and following his ouster, Bannon has given numerous interviews knocking Kushner, including one to my colleague Gabriel Sherman in which he questioned Kushner's maturity level.