Ms. James, whose office is also participating in the criminal investigation being run by the Manhattan district attorney Cyrus R. Vance Jr., wants to question Donald Trump on Jan. 7 as part of her separate civil inquiry into his business practices. If Ms. James finds evidence of wrongdoing in the civil inquiry, she could file a lawsuit against Mr. Trump, but she could not file criminal charges.

Ms. James´ request comes as Mr. Vance is pushing to determine whether Mr. Trump or his family business, the Trump Organization, engaged in criminal fraud by intentionally submitting false property values to potential lenders.

And because the two investigations overlap — both Ms. James and Mr. Vance have been focused on whether Mr. Trump inflated his property values to secure financing, and their offices are working together on the criminal inquiry — Mr. Trump could refuse to sit for a deposition once Ms. James formally subpoenas him.

Ronald P. Fischetti, a lawyer for Mr. Trump, said in a brief interview on Thursday that he would ask a judge to quash the subpoena.

Mr. Trump’s lawyers are likely to argue that the former president’s testimony could be unfairly used against him in the criminal investigation, violating the constitutional right against self-incrimination. If a judge sided with Ms. James, Mr. Trump could invoke his Fifth Amendment right and decline to respond to questions.

Danny Frost, a spokesman for Mr. Vance, said that Ms. James’s request was “not part of the criminal investigation.” He declined to elaborate and would not say whether Ms. James’s office had notified Mr. Vance’s prosecutors about the request to question Mr. Trump.

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