Mueller is investigating Russia's efforts to influence the 2016 election and whether President Donald Trump's campaign or associates colluded with the Kremlin as part of that effort, the newspaper said.
In an interview with a trio of NYT reporters at the White House last month, President Trump was asked if Mueller looking at his family finances would cross a "red line" of some sort: "I would say yes", the president replied, calling it "a violation" as the probe is about Russian Federation.
A former Justice Department official said Mueller's use of a Washington grand jury is a strong signal the Russian Federation probe has more than one line of inquiry cooking.
"We have been cooperating with Bob Mueller and his staff since the first of June because we're trying to get this thing over and done with", he said.
"This is yet a further sign that there is a long-term, large-scale series of prosecutions being contemplated and being pursued by the special counsel", said Stephen I. Vladeck, a law professor at the University of Texas told the Wall Street Journal. Meanwhile, the DOJ has yet to confirm any reports on this news.
The president's attorney says Mr. Trump has never discussed that with his legal team. Officials in Moscow have also denied playing a role in Trump's surprise victory last November.
The fact Mueller impaneled a grand jury doesn't mean one or more indictments are imminent, but it does provide some clues about where the investigation stands. In a statement Thursday, White House special counsel Ty Cobb claimed he didn't know Mueller had begun using the grand jury or issuing subpoenas.
In May Robert Mueller, a former director of the FBI, was assigned to the investigation.
Trump Jr has said he did not tell his father about the meeting.
White House spokeswoman Sarah Huckabee Sanders said the president was not likely the subject of the investigation, AFP reported.
It was reported on Thursday night, U.S. time, that he appointed the grand jury. United States intelligence agencies have concluded that Russian Federation attempted to sway the presidential contest in Trump's favor. He has also called the investigation a "witch hunt" and an attempt by Democrats to justify their loss in the election.
Rather a grand jury examines the evidence to determine if charges should be brought against someone.