Michael Cohen, the former personal attorney of President Donald Trump, departs the U.S. Capitol after testifying before a closed House Intelligence Committee hearing on Capitol Hill in Washington, February 28, 2019.

President Donald Trump's former personal lawyer and fixer Michael Cohen is formally cooperating with an investigation by the Manhattan District Attorney's Office into whether Trump's company falsified business records, a source familiar with the situation told NBC News.

Cohen, who is serving a three-year federal prison sentence for multiple crimes, is helping prosecutors in their probe of the Trump Organization as part of an effort to get a federal judge to reduce his sentence, another source familiar with the situation told CNBC on Thursday.

"He figures as much as he can help, the better," said CNBC's source of Cohen, whose proffer agreement allows him to share information with prosecutors without fear of having that information being used to file criminal charges against him.

Cohen has not yet formally asked his sentencing judge in his federal case to reduce his prison term.

Marc Mukasey, a lawyer for the Trump Organization, had a tart response to the news of Cohen's cooperation.

"When you lie down with dogs, you wake up with fleas," Mukasey told CNBC in an email.

On Aug. 20, representatives from the prosecutors' office, which is headed by DA Cyrus Vance Jr., went to meet with Cohen at the prison in Otisville, New York.

"Cy wants to go after the Trump Organization," the source said. "They're trying to get as much [evidence] as they can."

Cohen, who worked for Trump for years, has knowledge about hush money payments that he made to porn star Stormy Daniels and that American Media Inc., then-publisher of The National Enquirer, made to Playboy model Karen McDougal. The payments were made to keep the women quiet before the 2016 presidential election about their purported affairs with Trump years before.