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WASHINGTON, DC - JUNE 21:  Special counsel Robert Mueller (2nd L) leaves after a closed meeting with members of the Senate Judiciary Committee June 21, 2017 at the Capitol in Washington, DC. The committee meets with Mueller to discuss the firing of former FBI Director James Comey.  (Photo by Alex Wong/Getty Images)
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(CNN) —  

Special counsel Robert Mueller’s prosecutors have responded to the latest proposal from President Donald Trump’s legal team regarding a possible interview with the President, sources familiar with the matter said Tuesday.

The discussions for a possible presidential interview are continuing. The focus of the letter was an emphasis on written questions for the President, according to one source. Another source said Mueller’s letter stated the written responses would pertain to questions regarding potential conspiring between Trump associates and Russia. The response left unresolved the issue of an in-person interview and questions regarding Trump’s time in office, the source added.

The response was received on Friday, three-and-a-half weeks after the President’s lawyers submitted their last offer. Trump’s team hasn’t responded to the latest Mueller proposal.

The news of the Mueller team’s response comes the same day as excerpts from political reporter Bob Woodward’s latest book, “Fear: Trump in the White House,” became public.

In the book, Woodward describes a mock interview Trump did with his legal team, in which they hoped to prove to the President that he shouldn’t sit down with Mueller’s team for an interview. Trump’s lawyer at the time, John Dowd, viewed the interview as a disaster. According to Woodward, Trump seemed surprised by Dowd’s reaction and asked, “You think I was struggling?”

The Trump legal team’s position has been that any sit-down interview has to be limited to matters before Trump became President, and for questions related to possible obstruction and other post-inauguration matters to be done in writing.

While Trump’s lawyers have been against an interview, and the President has sounded less agreeable to talking lately, neither side has been willing to end the discussion. On Tuesday, the President called the Mueller investigation “illegal” in an interview with the Daily Caller.

In mid-August, the President called Mueller “highly conflicted” and said “let him write his report.”

Should the President refuse, Mueller could seek a subpoena to compel him to talk. That’s an effort that could lead to a Supreme Court challenge by the White House.

The Trump legal team view is that Mueller would be less likely to succeed in subpoenaing over issues of obstruction given executive privilege issues, for example, when it comes to the President’s discussions with Attorney General Jeff Sessions and Deputy Attorney General Rod Rosenstein about the firing of Comey, according to another source.

CNN’s Dana Bash, Jeremy Diamond, Allie Malloy, Marshall Cohen and Jamie Gangel contributed to this report.