Washington CNN  — 

Michael Cohen, former President Donald Trump’s former attorney, has handed over his cell phones to Manhattan prosecutors, he told “CNN This Morning” on Wednesday.

Prosecutors are zeroing in on the Trump Organization’s involvement in hush-money payments made to adult film star Stormy Daniels as part of an effort to stop her from going public about an alleged affair with Trump days before the 2016 presidential election. A grand jury in New York has been convened to hear evidence related to the effort, sources familiar with the matter have told CNN.

Cohen met last month with the Manhattan district attorney’s office. Trump has denied the affair.

“Most recently, they asked for my cell phones because they want to be able to extract from it the voice recordings that I had had with Keith Davidson, former attorney to Stormy Daniels before Michael Avenatti, as well as a bunch of emails, text messages and so on,” Cohen told CNN’s Don Lemon on Wednesday.

Cohen said the cell phones are “new to the district attorney,” despite being obtained by federal investigators after his home was searched by the FBI in 2018.

He also responded to the release of a video of a deposition Trump gave in August to the New York Attorney General’s office, in which he invoked his Fifth Amendment rights more than 400 times and declined to answer questions, according to multiple sources familiar with the matter.

“Donald cannot keep track of the lies that he tells, and so, what better way to stop a fool from being deposed and hurting himself further than to tell him to plead the Fifth at least 400 times,” Cohen said.

DA’s investigation heating up

Cohen’s disclosure on Wednesday is the latest in a series of signs that Manhattan prosecutors’ efforts to investigate the Daniels incident are heating up.

CNN has reported that former National Enquirer publisher David Pecker was set to meet with prosecutors this week as part of the probe. The district attorney’s office also reached out to Davidson, who represented Daniels in the hush money deal, in recent weeks.

Cohen pleaded guilty to federal campaign finance charges for facilitating the $130,000 payment to Daniels. Manhattan prosecutors are looking into whether Trump and his business falsified business records by improperly treating the reimbursement as a legal expense. That charge is a misdemeanor in New York unless it can be tied to another crime, such as campaign finance laws.

After Cohen made the $130,000 payment to Daniels, he was reimbursed, federal prosecutors said in court filings, by the Trump Organization. The company’s executives authorized payments to him totaling $420,000 to cover his original payment and tax liabilities, and reward him with a bonus, according to federal prosecutors. Prosecutors alleged the company falsely recorded those payments as legal expenses in their corporate books.

Cohen has said in court that hush-money payments were made at Trump’s direction, and federal prosecutors said that in executing the payments, Cohen “acted in coordination with and at the direction of” Trump.

Prosecutors working under the previous DA, Cy Vance, had explored bringing charges related to the hush money scheme but some attorneys on the team were not convinced that a charge involving a federal election law violation would survive legal challenges, people familiar with the investigation told CNN.

Last year, a jury convicted two Trump Organization entities of a decade-long tax fraud scheme, which appears to have emboldened prosecutors.

This story has been updated with additional reaction and background information.

CNN’s Kara Scannell and Paula Reid contributed to this report.