The Southern District of NY prosecutors also heard from Trump Organization lawyers, who want them to throw out all communication between Cohen, the company and its employees.
Cohen is also at the center of a legal dispute over alleged hush money payouts given to adult film actress Stormy Daniels, who alleges a sexual encounter with Trump over a decade ago.
In the filing with a court in NY, prosecutors blacked out a section describing what laws they believe Cohen has broken, but they said the "crimes being investigated involve acts of concealment" and suspected fraud.
In the Clifford case, Cohen and Trump on Friday filed a joint application requesting a 90-day stay of the action.
Not only would evidence that Cohen indeed traveled to Prague reveal he's been lying, but it would discredit the argument Trump and his allies in Congress have been using to discredit the Russian Federation investigation.
A spokesperson for him told CNN: "Attorney Davidson never consented to any recordings of his conversations with Mr. Cohen".
"Not at all. It's meant to send the message that this is a very, very serious matter for her and she wants to make sure that the American people know that she's behind efforts to bring to light as much information and documents as possible", he said.
Joanna Hendon, a new lawyer for Trump who appeared in court, said her law firm, Spears & Imes LLP, was engaged by Trump on Wednesday and she was "not prepared" to present her argument.
After three separate hearings on the matter Friday, U.S. District Court Judge Kimba Wood said she did not have enough information to issue any ruling on that request. The investigators intend to press Cohen for more information, the sources said.
The Justice Department is asking for a so-called taint team to vet the material seized in the raids Monday, as is standard process.
On Monday, Cohen's attorney called the searches "completely inappropriate and unnecessary".
White House spokesman Raj Shah said Friday evening that Michael Cohen continues to be President Donald Trump's personal attorney, despite being under criminal investigation. They cited the President's own comments.
Proof of Cohen's presence in Prague would amount to the strongest evidence yet that the Trump campaign colluded with Russian Federation to help Trump win the 2016 election.