Mr. Giuliani was also a central figure in the Trump campaign’s plan to urge lawmakers in swing states to appoint different slates of electors than those chosen by voters, which is part of the Georgia inquiry as well as the Justice Department investigation.
A spokesman for the Fulton County district attorney’s office declined to comment on Monday. It is unclear what charges Mr. Giuliani might face, should he be indicted. But in the past, Ms. Willis has said her investigation could result in racketeering or conspiracy charges involving multiple defendants.
Norman Eisen, a lawyer who served as special counsel to the House Judiciary Committee during the first impeachment and trial of Mr. Trump, said he believed that identifying Mr. Giuliani as a target could mean that Mr. Trump will eventually be a target as well.
“There is no way Giuliani is a target of the D.A.’s investigation and Trump does not end up as one,” Mr. Eisen said in an interview Monday. “They are simply too entangled factually and legally in the attempt to use fake electors and other means to overturn the Georgia election results.”
Lawyers for Mr. Giuliani have said that he did nothing improper in Georgia, and that he has been willing to cooperate. But they have been sparring with Ms. Willis’s office over her efforts to get him to testify before the grand jury. Mr. Giuliani’s lawyers have said a doctor recommended that Mr. Giuliani not travel by air because of a procedure he underwent in early July to insert cardiac stents, and they have sought to delay his testimony or have it conducted by video conference, an idea the district attorney’s office has resisted.
Judge Robert C.I. McBurney of Fulton County Superior Court said last week that Mr. Giuliani could travel to Atlanta “on a train, on a bus or Uber,” and set a date for Wednesday, after agreeing to delay his appearance for more than a week. Mr. Giuliani’s lawyers indicated that in any case, their client would have little to say if he was designated as a target of the investigation.