Special counsel Robert Mueller's investigators have asked witnesses questions about why President Trump never hired his longtime personal lawyer Michael Cohen for a job at the White House, according to a report Tuesday.

In the weeks after the April FBI raid into Cohen's office and residence, Mueller's team asked witnesses about Cohen's informal role as an adviser and surrogate for Trump's 2016 campaign and whether he conducted personal business while an employee of the Trump Organization, sources told CNBC.

Although it was Mueller who refereed the Cohen investigation to the U.S. Attorney's Office for the Southern District of New York, his investigators reportedly kept asking about Cohen until at least May.

The people who were questioned by Mueller's team told CNBC that they didn't have any information to share about Cohen's work during his time with the Trump Organization.

Last week Cohen, a former "fixer" for Trump, pleaded guilty to tax and bank fraud, and to campaign finance crimes he said were at Trump's direction.

CNN and other outlets reported last month that Cohen was prepared to tell Mueller that Trump had forewarning of the infamous Trump Tower meeting in which his son Donald Trump Jr. met with a Russian lawyer that was predicated with a promise of dirt on Democratic presidential candidate Hillary Clinton. However, those reports have been thrown in doubt as Cohen's lawyer, Lanny Davis, has come out in recent days to admit he was a source for those reports and admitted that he is unsure what Cohen actually knows about the Trump Tower meeting.

[Opinion: CNN’s Trump Tower scoop is falling apart]

Mueller's team is looking into possible collusion between Trump campaign officials and Russia.