Discussions between Special Counsel Robert Mueller's office and President Trump's legal team over the conditions of a possible presidential interview are ongoing, but have "not terribly advanced" from where they were a couple of weeks ago, a source familiar with the talks told Fox News Tuesday.

Also, The Associated Press reported that two prosecutors detailed to the Russia investigation for the past year are returning to their duties in other parts of the Justice Department. They join two other attorneys who left the team, assigned to investigate potential ties between Russia and the Trump campaign, over the summer.

Fox News' source said negotiations hit a snag when The New York Times reported on Sept. 21 that Deputy Attorney General Rod Rosenstein had discussed secretly recording Trump and enlisting Cabinet members to invoke the 25th Amendment to remove the president from office. Rosenstein has called the Times report "inaccurate and factually incorrect" and at least one source has told Fox News that Rosenstein intended his comment about recording Trump to be sarcastic.

"This Rosenstein thing really threw them for a loop," the source said in discussing the report's effect on the talks. Trump is tentatively scheduled to meet with Rosenstein at the White House later this week to discuss the report.

Trump's legal team previously proposed to Mueller that any presidential interview be limited to written questions and answers about allegations of Russian collusion with members of the Trump campaign. They also signaled opposition to questions about potential obstruction of justice, though the source told Fox News the president's attorneys now have left open the possibility of entertaining such questions "as long as they can be answered without jeopardy."

Mueller spokesman Peter Carr told the AP that prosecutor Brandon Van Grack already has returned to the Justice Department's national security division but will continue to be involved in cases to which he was assigned. That would include the investigation into former White House national security adviser Michael Flynn, who is scheduled to be sentenced in December.

Prosecutor Kyle Freeny will end her detail to the special counsel later this month and will return to her position in the Justice Department's money laundering section, Carr said.

Van Grack and Freeny were on the teams prosecuting Trump campaign chairman Paul Manafort.

The departures are the latest indication that Mueller's team is wrapping up parts of the investigation and focusing its efforts on critical remaining strands, including an active grand-jury probe of longtime Trump associate Roger Stone.

Elements of the Mueller investigation remain active, but other parts of the investigation have been referred to other offices of the Justice Department or largely taken over by them.

Prosecutors in Manhattan, for instance, secured a guilty plea in August from Trump's former personal lawyer, Michael Cohen, while prosecutors with the U.S. attorney's office in Washington have been assigned to the special counsel's case against 13 Russians charged in a hidden but powerful social media effort to sway American public opinion.

The U.S. Attorney's office in the District of Columbia also prosecuted W. Samuel Patten, who pleaded guilty to acting as an unregistered foreign agent in a case referred by Mueller's office.

Other lawyers who left the Mueller team earlier this year included computer crimes prosecutor Ryan Dickey, who worked cases against a Russian social media troll farm and 12 Russian intelligence officers accused of hacking Democratic groups during the campaign, and Brian Richardson.

Richardson was part of a team that prosecuted former Skadden Arps attorney Alex van der Zwaan for lying to the FBI while the team was investigating Manafort and others involved in his Ukrainian work. Van der Zwaan was sentenced to 30 days behind bars.

Fox News' John Roberts and The Associated Press contributed to this report.