The lack of transparency around documents that could potentially show improper use of the Steele dossier might be justifiably confounding for the president, Wisenberg said. "But there's no no mystery about the fact that he's livid at [Attorney General Jeff] Sessions for recusing himself and livid at Rosenstein for appointing a special counsel."
It could also be the case, multiple experts said, that Trump hopes firing the deputy attorney general will allow him to appoint someone more amenable in Rosenstein's place.
Rosenstein has been an occasional target of Trump's criticism since Mueller's appointment in May 2017.
On Monday, Bloomberg reported that Trump became angry on his flight to the World Economic Forum in Davos, Switzerland, after learning that a Justice Department official sent a letter warning against a public release of the House Republicans' memo on alleged FISA abuses. Trump considered the letter another example of the Justice Department's political motivations, sources told Bloomberg.
Justice Department officials, the memo reportedly says, weren't clear enough when applying for the warrant that their information came, in part, from the Steele dossier.
Daniel Farber, a professor of constitutional law at Berkeley Law School, said that misrepresenting the warrant application would be one of the only ways Rosenstein's Justice Department could be accused of misconduct in this scenario.
"Let's say he's relying on material but he attributes it to the CIA rather than an outside source. He would be intentionally misrepresenting facts," Farber said, though he considered it unlikely. "I would be surprised," he said.
Trump and some Republicans have decried the memo, parts of which are reportedly unverified, as being a politically motivated fabrication.
While the right-leaning Washington Free Beacon said it was the first to commission Fusion GPS to investigate Republican primary candidates in 2016, Steele was later paid by the Democratic National Committee, the presidential campaign of former Secretary of State Hillary Clinton and the FBI.
On Monday, White House press secretary Sarah Huckabee Sanders denied that Trump had lost confidence in Rosenstein:
"When the president no longer has confidence in someone, you'll know."