On Monday, grand jurors heard more than two hours of testimony from Robert Costello, an attorney for Trump ally Rudy Giuliani.
Instead, Cohen waited outside the grand jury room Monday, at the ready should he be called before the grand jury again to challenge Costello's testimony, Davis said.
The grand jury would still need to be "charged," the process when prosecutors explain the potential indictment count by count.
Following the charge, the grand jurors would deliberate and vote.
Grand jurors frequently accomplish these tasks quickly, according to former Manhattan prosecutor John Moscow, who handled hundreds of white-collar criminal cases before going into private practice.