A judge had set a deadline of Friday for Cohen's legal team to finish its review of the seized documents.
A retired judge is reviewing more than 3.7 million items seized in the Federal Bureau of Investigation search to determine whether they should be held back from investigators because they are privileged attorney-client communications or are personal.
Trump's lawyers have resigned themselves to the strong possibility that this investigation could lead Cohen to cooperate with prosecutors.
Read the full report at ABC News. (Reached for comment, Cohen wrote in a text message, "Your alleged source is wrong!") The specter of Cohen flipping has Trump advisers on edge.
The investigation is reported to be regarding possible campaign finance violations related to the $130,000 payment made to adult film star Stormy Daniels in exchange for her silence regarding an affair she claims to have had with Trump.
The AP reports federal prosecutors in NY have publicly said they are investigating alleged fraud in Cohen's business dealings, but haven't disclosed details.
"Trump should be super anxious about Michael Cohen [flipping]", a former White House official said, noting, "If anyone can blow up Trump, it's him".
Rudy Giuliani, another member of Trump's legal team, said last month that Cohen was no longer representing Trump.
The source said Cohen had not yet met with prosecutors to speak about a potential deal, and it's unclear whether either side is seeking one.