(CNN) Attorneys for former Obama White House counsel Greg Craig gave a presentation in recent months to federal prosecutors in New York who are weighing criminal charges against their client for failing to register as a foreign agent, according to people familiar with the matter.

The presentation by lawyers for Craig, who until earlier this year was a partner at the high-profile law firm Skadden, Arps, Slate, Meagher & Flom LLP, signals how seriously his attorneys consider the inquiry by the US Attorney's Office for the Southern District of New York.

That office received the case as a referral from special counsel Robert Mueller's office earlier this year, in a matter related to the prosecution of former Trump campaign chairman Paul Manafort, and in recent weeks has considered bringing criminal charges against Craig, CNN has previously reported

An attorney for Craig declined to comment. A spokeswoman for Skadden declined to comment.

The query has to do with whether Craig, in his work at Skadden for Ukraine, improperly failed to file under the Foreign Agents Registration Act, which requires that an entity representing a foreign political party or government file public reports detailing the relationship.

A presentation to prosecutors by defense counsel is generally encouraged by the Southern District office, said Carrie Cohen, a former prosecutor in the office's public-corruption unit, and such sessions are typically used by the defense side to either try to help shape prosecutors' view of the evidence or highlight uncertainties or weaknesses in legal theories.

They can also be used to explain conduct or to "appeal to the office's sense of prosecutorial discretion," she said.

The office "takes defense presentations very seriously and takes what they say into consideration in their final charging decision," Cohen said. She added that "these situations can evolve very quickly into plea discussions."

The inquiry into Craig and Skadden and those into the lobbying firms Mercury Public Affairs and the Podesta Group -- and two of their employees, Podesta Group co-founder and longtime Democratic lobbyist Tony Podesta and Mercury partner and former Minnesota Republican Rep. Vin Weber -- are linked closely to a special counsel case against Manafort, in which Manafort pleaded guilty to conspiracy, admitting to lobbying illegally for Ukrainian politicians in the US, and agreed to cooperate with the federal government.

Manafort and his attorneys have met with the special counsel's office prosecutors on eight days since his guilty plea last month, suggesting that he's given the Justice Department an extensive amount of information. He will be in court in Virginia on Friday to discuss the timing of his first round of sentencing.

In New York, however, the cases involving Podesta and Weber do not appear to have made serious advancements, with no significant investigative steps having been taken in recent months, according to people familiar with the matter.

An attorney for Weber declined to comment. A spokesman for Mercury declined to comment. A spokeswoman for Podesta declined to comment.

The superseding indictment in the Manafort case contains lengthy sections detailing the involvement of an unnamed law firm -- previously identified by CNN as Skadden -- and two unnamed lobbying firms -- previously identified by CNN as Podesta and Mercury -- in Manafort's efforts on behalf of the then-president of Ukraine, Viktor Yanukovych.

The Manafort indictment alleged that he "solicited" the law firm on behalf of Yanukovych and the Ukranian government's Ministry of Justice, and that the firm was paid more than $4.6 million for both its representation of Ukraine and for a report it wrote on the trial of Yulia Tymoshenko, the former prime minister of Ukraine and political rival of Yanukovych. Craig was the firm partner who worked on that report, CNN has reported.

The indictment also alleged that employees of the two lobbying firms knew they were working for Ukrainian politicians and not an independent nonprofit group.

Mercury filed a different form of disclosure instead of filing under the Foreign Agents Registration Act, and has said it did so on the advice of its counsel, who was another attorney at Skadden. The Podesta firm also filed a different form of disclosure, and has said it did so both because the group it was working for had misrepresented itself and due to an opinion by outside legal counsel.