The office of the Manhattan district attorney, Cyrus R. Vance Jr., first began investigating Mr. Manafort in 2017 in connection with loans he received from two banks. Those loans were also the subject of some of the counts in the federal indictment that led to his conviction last year. But the state prosecutors deferred their inquiry in order not to interfere with Mr. Mueller’s investigation into Russian interference in the 2016 presidential election.

They resumed their investigation in recent months, and a state grand jury began hearing evidence in the case, several people with knowledge of the matter said. The panel is expected to wrap up its work in the coming weeks, several of the people said, and prosecutors likely will ask the grand jurors to vote on charges shortly thereafter.

Mr. Vance’s office is expected to seek charges whether or not the president pardons Mr. Manafort. The plan was first reported by Bloomberg.

Any charges brought by Mr. Vance’s office would likely be challenged on double jeopardy grounds. New York state law includes stronger protections than those provided by the United States Constitution, and Mr. Manafort’s defense team is likely to challenge any state charges. But prosecutors in Mr. Vance’s office have expressed confidence that they would prevail, people with knowledge of the matter said.

Former Trump campaign chairman Paul Manafort “repeatedly and brazenly violated the law” and shows a “hardened adherence to committing crimes,” prosecutors told a Washington federal judge.

They recommended no specific punishment for those crimes, saying that is the practice of the special counsel. Prosecutors noted that federal guidelines call for a sentence of 17 to 22 years, although under Manafort’s guilty plea in his D.C. case, the statutory maximum he faces is 10. The special counsel said that they may ask for Judge Amy Berman Jackson to impose a sentence that runs consecutive to whatever punishment Manafort is given for related crimes in Virginia federal court.

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Jackson found Manafort lied about his interactions with Konstantin Kilimnik, a longtime aide who the FBI assessed to have ties to Russian intelligence. Those contacts, prosecutors said in court, go “very much to the heart of what the special counsel’s office is investigating.”

Manafort gave inconsistent accounts of an August 2016 meeting in New York City at which he and Kilimnik discussed a peace plan for Ukraine, a top foreign policy priority for Russia. At the time, Manafort was still leading President Trump’s campaign. He also lied about sharing polling data with Kilimnik in 2016, prosecutors said in describing how he broke his deal to cooperate truthfully.

The judge also concluded that Manafort lied about a payment that he claimed was a loan and as part of another Justice Department investigation whose focus has not been described publicly.