(CNN) Michael Cohen has been making the rounds since his late-August guilty plea in federal court, offering himself up to a number of offices that are investigating him or other aspects of the Trump orbit.

And on Friday, Cohen set off fresh speculation when he made an unexpected appearance in Manhattan federal court, where defendants typically sit for interviews before their sentencing.

But it's not clear what President Donald Trump's former personal attorney can provide prosecutors or others probing these matters -- and it's uncertain Cohen will receive any benefit in return.

He has met with prosecutors from the office of special counsel Robert Mueller, where he provided "critical information" to that investigation, an attorney and adviser to Cohen, Lanny Davis, said Thursday night on Twitter.

Prosecutors from the US Attorney's Office for the Southern District of New York, who charged Cohen in August, had been seeking to arrange for him to sit down with them, according to a person with knowledge of the matter, and former prosecutors familiar with the process said it was likely that those from the US attorney's office would have participated in Cohen's sessions with the Mueller team, given that the two sets of prosecutors have different investigative interests and different areas of expertise.

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