Dean's comments, made during CNN's "Erin Burnett OutFront" segment, follow the release of a legal memo from federal prosecutors in NY regarding Trump's former personal lawyer, Michael Cohen.
Trump has made little secret of his frustration with the swirling probe into Russian election interference and potential misdeeds committed by those in his orbit and is seeking to undermine the legitimacy of Mueller's investigation.
Dean, who served as Nixon's counsel from 1970 to 1973, was chosen by the president to lead a special investigation into the Watergate scandal.
Court filings Friday from prosecutors in NY and special counsel Robert Mueller laid out why Michael Cohen, U.S. President Donald Trump's former personal lawyer, and Paul Manafort, Trump's former campaign manager, deserve prison time.
The memo from NY prosecutors identifies three people at an August 2014 meeting: Cohen, "Individual 1" and "Chairman 1".
"In total, the prosecutors seem to be saying the president was more aware than he has claimed to be", former federal prosecutor Michael Zeldin said.
"These legal documents outline serious and criminal wrongdoing, including felony violations of campaign finance laws at the direction of President Trump", Senator Diane Feinstein said in a statement.
Mueller is investigating whether there was collusion between Trump's 2016 presidential campaign and Russian Federation, which U.S. intelligence agencies charge mounted an influence operation to sway the vote to Trump over his Democratic rival, Hillary Clinton.
Last week, Cohen admitted to lying to congressional investigators in an attempt to minimize his efforts to secure the Kremlin's help for a Trump skyscraper in Moscow.
But also, significantly, the memo documents Cohen's claims that he was operating at the behest of Trump when he paid off two women Trump allegedly had affairs with to keep them from going to the press during the 2016 presidential campaign.
The filing says the meeting never happened.
The commander-in-chief vowed his lawyers would produce a "major Counter Report" to rebut Mueller's findings, as and when he delivers them.
Mueller also detailed alleged lies told by Manafort during interviews with prosecutors and the Federal Bureau of Investigation.
Manafort has said he believes he provided "truthful information".
Cohen also told prosecutors that he and Trump discussed a potential meeting with Putin on the sidelines of the U.N. General Assembly in 2015, shortly after Trump announced his candidacy for president, the filings say.
Cohen had been hoping prosecutors would make a similar recommendation in his case.
Cohen continued to provide "relevant and truthful information" to assist the probe, holding seven sessions with investigators, "many of them lengthy, and continues to make himself available to investigators", it said.
US Attorney Robert Khuzami accused the 52-year-old, who once vowed to take a bullet for the president, of being motivated by "personal greed" and of "repeatedly" using his power and influence for "deceptive ends". They said his sentence should reflect a "modest" reduction from the roughly four to five years they said federal guidelines would suggest.
Mueller, for his part, praised Cohen for voluntarily providing information about his own and others' conduct on "core topics under investigation" and described the information as "credible and consistent with other evidence" they had obtained.
Due to his help, Mueller declined to recommend additional jail time for Cohen for lying to Congress.