ST. LOUIS — The potential jurors stole curious glances at Gov. Eric Greitens, the defendant, whose famous face usually appeared in glossy campaign ads. They told the courtroom they had already heard about the case before them, picking up scraps about his indictment in break rooms at work, on the Channel 5 news, watching YouTube videos and scrolling through Facebook feeds. Some seemed not to need to hear more.

“You believe Governor Greitens isn’t truthful?” Scott Rosenblum, a lawyer for the governor, asked a prospective juror who said she got her news mostly from local television. “How long have you held that opinion?”

“Since the case has come up,” she answered.

Minutes later, she was sent home.

For hours on Thursday and Friday, Judge Rex Burlison and two teams of lawyers meticulously questioned St. Louis residents in a search for an impartial jury that had not already decided on the guilt or innocence of their embattled governor. It was no simple task. Publicity may be the highest aspiration of politicians seeking voters; less so, it turns out, for a criminal defendant in search of jurors.

Mr. Greitens, whose brief governorship has been consumed with scandal and the threat of impeachment, is to be tried next week on one felony count of invasion of privacy. Prosecutors contend that in 2015, he took an explicit photograph of a woman without her consent; the two were having an extramarital affair. If convicted, he faces up to four years in prison.