If this is true, it could heighten the credibility of the so-called Steele dossier, an unverified set of memos that contain allegations that members of the Trump campaign colluded and conspired with Russian Federation during the presidential campaign.
The already complex legal battle could soon see another layer of litigation, as former Clifford attorney Keith Davidson has threatened to sue following reports that Cohen recorded their phone conversations without his knowledge.
Mr Cohen had already notified the US District Court in Los Angeles on Thursday that he meant to request a stay in Ms Daniels' lawsuit against him and Mr Trump "on the grounds that an ongoing criminal investigation overlaps with the facts of this case".
"[Fusion GPS] recklessly placed it beyond their control and allowed it to fall into the hands of media devoted to breaking news on the hottest subject of the day: the Trump candidacy", read the lawsuit filed in NY state court. The news service, quoting anonymous sources, reports that Mueller can prove Cohen visited Prague in 2016 in the midst of the election.
Avenatti predicted Sunday that Cohen will face criminal charges in the "next 90 days" possibly related to bank fraud, wire fraud and campaign finance violations.
Before Trump's election, Cohen spent nearly a decade in high-profile positions in Trump's real-estate company and built a reputation as Trump's fixer.
Cohen previously, whose real name is Stephanie Clifford, to keep her from sharing details of an alleged 2006 affair with Trump.
White House Press Secretary Sarah Huckabee Sanders followed Trump's comments on Mueller by stating the president "certainly believes he has the power" to fire the special counsel, in a comment that appeared to go against the Code of Federal Regulations' guidance that a special counsel can only be dismissed by the attorney general.
They were in court Friday trying to stop federal prosecutors from getting private documents. In response, prosecutors said they have set up a "taint team" to review documents before attorneys working on the case can access them.
He added: "She also wants to ensure that she is heard and that she's represented at the hearing". The judge requested that Cohen be present in court on Monday.
"It's meant to send the message that this is a serious matter for her and she wants to make sure that the American people know that she is behind efforts to bring to light as much information and documents as possible", Avenatti said.
Michael Avenatti, a lawyer for Stormy Daniels, also made an appearance at the hearing.