Meanwhile, Ellis has denied a request to relocate Manafort's trial.
Former Trump campaign manager Paul Manafort is shown in this booking photo in Alexandria, July 12.
Mueller's office told a federal judge in Virginia on Tuesday that they were seeking to compel the witnesses to testify under condition of immunity.
The decision to grant immunity would in theory prevent witnesses from refusing to answer specific questions when testifying against Mr Manafort.
Manafort faces numerous charges, including conspiracy to commit money laundering, making false statements and working as an unregistered agent of the government of Ukraine.
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Mueller says the witnesses haven't been publicly identified in the case, and haven't been charged.
U.S. District Judge T.S. Ellis denied a motion filed by Manafort's attorneys to move the Virginia trial, scheduled for later this month, from Alexandria, Va., to Roanoke, Va., over his claims that relentless media coverage of his role in the Trump campaign and by extension the Russian Federation investigation would taint a potential juror pool.
Manafort's trial before Washington, D.C., District Court Judge Amy Berman Jackson is expected to take place in September.
The lawyers cited extensive pretrial publicity in the case and the fact that potential jurors in Alexandria were more likely to have supported Hillary Clinton than Trump in the 2016 presidential election.
Manafort is facing charges in two separate cases.