"Not only is he not hoping for it, he would not accept a pardon. He considers a pardon from somebody who has acted so corruptly as president to be something he would never expect," Davis said in an interview on NBC's "TODAY."
The White House did not immediately respond to CNBC's request for comment on Davis' remarks.
Davis also said Cohen is willing to share information with special counsel Robert Mueller, who is investigating Russia's attack on the 2016 campaign and any potential conspiracy between the Kremlin and the Trump campaign to sway the election.
Cohen "is more than happy to tell the special counsel all that he knows, not just about the obvious possibility of a conspiracy to collude and corrupt the American Democracy system in the 2016 election, ... but also knowledge about the computer crime of hacking and whether or not Mr. Trump knew ahead of time about that crime and even cheered it on," Davis told MSNBC's Rachel Maddow.
Comments from Davis, who served in the White House under President Bill Clinton and remains close to the Clinton family, came after Cohen pleaded guilty in federal court in New York on Tuesday to eight felony counts of tax fraud, bank fraud and campaign finance violations.
The U.S. Attorney's office said Cohen pleaded guilty for facilitating payments to prevent two women from discussing their "alleged affairs with a presidential candidate, thereby intending to influence the 2016 presidential election."
Mueller, as part of his election meddling probe, had referred the Cohen case to federal prosecutors in Manhattan.
Cohen's plea came as a federal jury in Alexandria, Virginia, convicted former Trump campaign chairman Paul Manafort on eight counts of fraud and other charges.
"I feel very badly for Paul Manafort," Trump said Tuesday after landing in West Virginia for a campaign rally. But he added the conviction "doesn't involve me" and has "nothing to do with Russian collusion."
The president did not comment on Cohen's plea deal, and did not mention either Cohen or Manafort during his speech at the rally Tuesday night.
Trump broke his silence on Cohen on Wednesday morning, however.
"If anyone is looking for a good lawyer," the president tweeted, "I would strongly suggest that you don't retain the services of Michael Cohen!"