(CNN) Federal prosecutors are close to bringing charges against Greg Craig, a prominent Democratic lawyer and former White House counsel in the Obama administration, in a case that originated with special counsel Robert Mueller, according to people familiar with the matter.

The possible charges are connected to false statements Craig allegedly gave to investigators who were looking at the work he performed for Ukraine.

Though Mueller's investigation has ended, a number of inquiries that were referred out by his office live on in other prosecutors' offices, and Craig's is among the earliest and most unusual.

A review of the case against Craig, much of it previously unreported, demonstrates the tumultuous path of the investigation of one of the country's most prominent attorneys, a matter that has gone on for so long and changed hands so many times that the statute of limitations for the initial matter for which he was investigated -- failure to register as a foreign agent -- has expired.

This story is based on information from six people familiar with the government's investigation, which is now in the hands of the Justice Department's national security division and the US Attorney's office for the District of Columbia.

A spokesman for the national security division declined to comment. A representative for the US Attorney's office for the District of Columbia did not respond to a request for comment.

Craig's attorneys, William Taylor and William Murphy, said: "If the National Security Division stubbornly insists on prosecuting Mr. Craig, any such charges would be a misguided abuse of prosecutorial discretion."

Craig initially came into the crosshairs of federal prosecutors in mid-2017, during the investigation by Mueller. Craig and his then-firm, Skadden, Arps, Slate, Meagher & Flom LLP, had performed work beginning in 2012 for Ukraine's Ministry of Justice. It was a client relationship the Justice Department has said was forged with the assistance of Paul Manafort, who later became President Donald Trump's campaign chairman.

The special counsel team was intrigued by the notion of using a once-obscure law, the Foreign Agents Registration Act, or FARA, to pursue cases of individuals acting as unregistered foreign agents, a charge the special counsel subsequently brought against Manafort and his business partner, Rick Gates, both of whom have since admitted to failing to register as foreign agents for their work for Ukraine. Craig and Skadden, during the course of their work for Ukraine, hadn't registered under FARA.

Craig was interviewed twice by the special counsel team -- once in the fall of 2017, at which time he was represented by Skadden's general counsel, and a second time in March 2018, by which point he had retained his own counsel. Days after the second interview, special counsel prosecutor Andrew Weissmann informed Craig that his case was being transferred to the US Attorney's Office for the Southern District of New York.

The impression Craig's attorneys were given was that the special counsel was concerned about staying within the scope of its mandate. The case concerning Craig was transferred alongside two related inquiries, CNN has reported.

Presentation to prosecutors

The US attorney's office appeared to be devoting significant resources to the matters. Craig's attorneys held a series of meetings with federal prosecutors from Manhattan and the Justice Department's national security division beginning in late August 2018 that included a detailed presentation the lawyers gave to the US Attorney's office in early September.

In attendance at an hours-long meeting in Manhattan in early September were US Attorney Geoffrey Berman, deputy US Attorney Rob Khuzami and the office's chief counsel Audrey Strauss, as well as more than a dozen other prosecutors.

At issue was contact Craig made in late 2012 with several newspaper reporters the time of the public release of a report he had written for Skadden's client, the Ukranian Ministry of Justice, on the trial of Yulia Tymoshenko, the former prime minister of Ukraine. The inquiry from prosecutors concerned whether Craig had contacted reporters on behalf of Ukraine to distribute the report to the reporters and whether he had subsequently provided false information to the Justice Department's FARA unit when he met with representatives from the unit in October 2013.

Craig's attorneys emphasized to Berman and the others that when Craig spoke to reporters, in particular to a New York Times reporter who wrote an initial story on the report, it was for the purpose of preventing what he believed would be a mischaracterization of the document, and didn't coordinate his outreach with Ukraine's Ministry of Justice.

They also pointed out that Craig didn't bill for that outreach because he didn't believe he was acting on behalf of Ukraine. And they maintained to prosecutors that his contact with reporters was to correct the impression that the report was favorable to Ukraine, a step that ran contrary to Ukraine's interests.

Finally, they raised concerns that Craig, a prominent Democrat, was being examined in part to due to the political climate and to compensate for an investigative emphasis on Trump-connected Republicans as a result of Mueller's probe. Craig's attorneys also sent lengthy written submissions and subsequent written memos outlining these points.

In the fall of 2018, the US Attorney asked Craig's attorneys to extend the statute of limitations on the FARA inquiry, a practice known as tolling. It was weeks before the midterm elections, and Craig's attorneys raised concerns that they were being asked to extend the statute simply so that the office could avoid the choice of whether to indict Craig on the eve of an election. Berman promised that wasn't the case, and Craig agreed to extend the statute for 90 days.

According to people familiar the matter, New York federal prosecutors determined they didn't have sufficient evidence to bring charges against Craig.

A spokeswoman for the US Attorney's office for the Southern District of New York declined to comment.

In early January, days before the tolling agreement was set to expire, national security division prosecutors informed Craig's team that his case had been transferred again, this time to the US Attorney's office for the District of Columbia. Craig's attorneys made another presentation, this time in early 2019 to prosecutors from that office and the national security division.

Skadden makes a deal

This January, however, the Justice Department's national security division disclosed that it had settled with Skadden in an agreement that forced the firm to turn over $4.6 million it earned for its 2012 work for Ukraine and to retroactively register as a foreign agent. The language of the settlement appeared to leave Craig exposed to potential criminal charges for what the document describes as his repeated "false and misleading" statements to Justice Department officials.

No notes were taken during Craig's meeting with the FARA unit in 2014 in which prosecutors allege he made false statements, however. Rather, the Justice Department appears poised to charge Craig based on his own recollection of what was said in the meeting, which he conveyed in a letter he composed afterward.

In recent weeks, Justice Department prosecutors have privately suggested that Craig enter into a plea deal.

He has rejected that option.