Daniels, whose real name is Stephanie Clifford, has sought to intervene in the case, saying some of the seized materials could relate to her. Daniels has said Cohen paid her $130,000 to keep quiet about a sexual encounter she had with Trump, which Trump has denied.
The BBC said the payment to the NY lawyer was at least $400,000 for making the sit-down happen.
Michael Avenatti - who has uncovered details of Mr Cohen's finances - said Suspicious Activity Reports filed by Mr Cohen's bank to the US Treasury showed he had received money from "Ukrainian interests", according to the BBC.
According to the BBC, several sources in Ukraine said Mr Poroshenko, believing Democratic candidate Hillary Clinton was sure to win the presidency, had authorised the leak of a document published by the New York Times in August 2016.
Mr. Trump's lawyers have been resigned to the strong possibility that the investigation of Mr. Cohen's businesses could lead him to cooperate with federal prosecutors. Trump, whose spokesmen have denied such an affair, reimbursed Cohen for the payment to Daniels.
Brandi Chastain's Hall of Fame plaque looks like Gary Busey or something
The Bay Area Hall of Fame is a nonprofit that honors local athletes and awards grants for at-risk young people to play sports. Other people had plenty of feelings about what Chastain's plaque looked like, and not all of them were as kind as mine.
Friedman, dubbed the "Taxi King", has reportedly for years managed Cohen's taxi companies in NY and Chicago.
A high-ranking Ukrainian intelligence officer told the BBC that Cohen was brought in to arrange the Oval Office sit down because Ukraine's registered lobbyists and the embassy in Washington DC could only get Poroshenko a brief photo-op with Trump.
Freidman also denied that his own legal situation had anything to do with the NY state criminal investigation into Cohen's business dealings, saying he hates "that I have been grouped in this runaway train that I am not a part of!"
Freidman had been the largest operator of medallions in New York City, with his company, Taxiclub, reportedly boasting a fleet of more than 800 cabs.
Freidman struggled financially as the value of taxi medallions plummeted. That likelihood may now be greater, with Mr. Freidman potentially sharing what he knows with federal prosecutors in NY and the special counsel. Instead, he filed false tax returns created to hide the theft, they said.
Word of the Freidman agreement came just days after news broke that Jeffrey Yohai, the son-in-law of former Trump campaign chief Paul Manafort, had reached a plea agreement. "Friedman pocketed money that should have provided much-needed investment in our transit system and he'll now have to pay back every cent". In pleading guilty to a single count of criminal tax fraud, Freidman will be sentenced to five years' probation, the attorney general's office said.