The jury verdict landed within minutes of Cohen pleading guilty to eight charges of tax evasion, bank fraud and campaign finance violations.
According to his remarks on Maddow's show, Davis said that Cohen is willing to tell Mueller what he knows about the "possibility of a conspiracy to collude and corrupt the American democracy system in the 2016 election" and also what Trump knew about computer hacking.
Lanny Davis, Mr. Cohen's attorney, said on Twitter: "Today he stood up and testified under oath that Donald Trump directed him to commit a crime by making payments to two women for the principal objective of influencing an election".
His plea came as former Trump campaign chairman Paul Manafort was found guilty on eight charges in his financial fraud trial stemming from the federal investigation into Russian meddling in the 2016 USA election and possible coordination with the Trump campaign. "Fake news and the Russian witch hunt..."
He also did not name Trump, but said it was "in coordination and at the direction of a candidate for federal office", and the other was made "under direction of the same candidate".
Mr. Davis told CNN that Mr. Cohen has information that would be useful for Mr. Mueller's investigation. As the New York Post noted, Davis said in an interview on MSNBC that his client has knowledge on certain subjects that would be of great interest to the investigation.
"The likelihood of me getting a deposition of the President of the United States under oath just went through the roof - no question about it".
According to Davis, Cohen feels motivated in part because of Trump's controversial news conference with Russian President Vladimir Putin earlier this summer in Helsinki, Finland, during which Trump appeared to side with Putin over the US intelligence community on Russian interference in the election.
Cohen's extraordinary account marks the first time that any Trump associate has gone into open court and implicated Trump himself in a crime, though whether-or when-a president can be prosecuted remains a matter of legal dispute.
That two-pronged approach continued after Cohen's guilty plea.
Cohen's attorney is Lanny Davis, former White House special counsel to President Bill Clinton.
Working out of a Trump Tower office next to his boss, Cohen likely has vast knowledge of the inner workings of Trump's empire, his business dealings and his campaign.
By most counts, Tuesday was not a good day for President Donald Trump. "'Unlike Michael Cohen, he refused to 'break" - make up stories in order to get a 'deal".
After bashing Cohen Wednesday morning, Trump praised Manafort, saying, "Unlike Michael Cohen, [Manafort] refused to "break" - make up stories in order to get a 'deal.' Such respect for a courageous man!"
"My message to the president: you better not talk about pardons for Michael Cohen or Paul Manafort tonight, or anytime in the future", Schumer wrote on Twitter Tuesday.
The legal developments also increase pressure on Trump personally. "This has nothing to do what they started out, looking for Russians involved in our campaign". "There are many, many steps that need to be taken before the president is in legal jeopardy".