Mr. Giuliani, who spearheaded efforts to keep Mr. Trump in power as his personal lawyer, emerged in recent weeks as a central figure in the inquiry being conducted by Fani T. Willis, the district attorney of Fulton County, Ga., which encompasses most of Atlanta. Earlier this summer, prosecutors questioned witnesses before a special grand jury about Mr. Giuliani’s appearances before state legislative panels in December 2020, when he spent hours peddling false conspiracy theories about secret suitcases of Democratic ballots and corrupted voting machines.

For Mr. Giuliani, the former mayor of New York, the developments are the latest in a widening swath of trouble, though he got some good news recently when it emerged that he was unlikely to face charges in a federal criminal inquiry into his ties to Ukraine during the 2020 presidential campaign.

Mr. Giuliani is scheduled to appear before the special grand jury on Monday at a downtown Atlanta courthouse. His lawyer, Robert Costello, disclosed in an interview that prosecutors told him Monday that Mr. Giuliani was a target.