He noted that Attorney General William Barr, who under regulation has discretion about which parts, if any, of a final report he releases.
The president also claimed Wednesday that Mueller's "best friend is Comey, who's a bad cop", referring to James B. Comey, whom Trump fired as Federal Bureau of Investigation director.
Scrubbing the report for executive privilege claims is well within the purview of the White House counsel's office - after all, their charge is to defend the institution of the presidency, not the individual President they serve.
Trump, of course, nominated Rosenstein, who was confirmed by the Republican-controlled Senate in a 94-6 vote.
The CNN/SSRS poll released on Wednesday found that 87% of Americans believe that the Mueller report should be made public. Democrats have launched a sweeping probe of Trump, an aggressive investigation that threatens to shadow the president through the 2020 election season.
FILE - Former FBI Director James Comey, with his attorney, David Kelley, right, speaks to reporters after a day of testimony before the House Judiciary and Oversight committees, on Capitol Hill in Washington, Dec. 7, 2018.
Comey claimed that Trump asked him to shut down an investigation of former national security adviser Michael Flynn.
"That's why this whole debate about whether Rod Rosenstein was joking when he said "I'll wire up against the president" or not sort of rung in my ear a little bit".
But the evidence so far shows that a broad range of Trump associates had Russia-related contacts during the 2016 presidential campaign and transition period, and several lied about the communications.
Comey, who oversaw the FBI's collusion investigation for more than nine months until his firing, said that he has "no idea" whether Mueller will conclude that Trump knowing colluded with Russian Federation.
"But it's sort of an awesome thing that when you had a great victory, somebody comes in, does a report out of nowhere, tell me how that makes sense, who never got a vote, who the day before he was retained to become special counsel, I told him he would be working at the FBI", Trump said.
Trump's tweeted version was even more graphic: The Democrats' House investigative committees were going "stone cold insane". "I mean, frankly, I told the House, 'If you want, let them see it'". Trump has denied collusion and obstruction.
The plan is clear: Delegitimize Mueller personally and professionally, paint his findings as a deep state coup that trashes votes of his millions of Trump supporters, and argue that he's bulletproof since he's doing such a great job.