The development reported late on Tuesday signals that the Manhattan district attorney's office was moving toward seeking charges as a result of its two-year investigation, which included a lengthy legal battle to obtain Trump's tax records.
This news was first published by the newspaper Washington Post, It cited two people who knew about the matter, the arbitral tribunal was recently formed and is expected to work for about six months.
Vence's office said in court filings that it was investigating "probably widespread and protracted criminal activity" at the Trump Organization.
In February, Trump said the probing by James and Vance Jr. was a witch hunt and denied any wrongdoing, calling the investigation a "new phenomenon of "headhunting" prosecutors and AGs".
A spokesman for Vance's office declined to comment on the Post report.
"This is purely political, and an affront to the nearly 75 million voters who supported me in the Presidential Election, and it's being driven by highly partisan Democrat prosecutors".
Investigators suspect the Trump Organization may have artificially inflated and reduced the value of assets, particularly several properties in NY state, to either get bank loans or reduce their taxes.
The Trump Organization's longtime chief financial officer Allen Weisselberg has been named in multiple reports as a pressure point, eyed by Manhattan prosecutors as someone who could potentially cooperate against the former president.
A special grand jury sits for a longer period of time.
According to the Associated Press, one source says Vance's investigation into Trump involves "a variety of matters such as hush-money payments paid to women on Trump's behalf, property values and employee compensation".
In recent months, Vance has hired former Mafia prosecutor Mark Pomeranz to assist in conducting the investigation and interviewed witnesses, including former Trump private lawyer Michael Cohen. An election next month is all but certain to determine who that will be.
Vance fought twice to the US Supreme Court to access eight years' worth of Trump's personal and business tax returns.
Allen Weisserberg was summoned in a James civil investigation and witnessed twice past year. His former daughter-in-law, Jen Weisselberg, is cooperating with both inquiries.
Mr Trump has not been criminally charged.
Trump issued a statement last week complaining that he's being "unfairly attacked and abused by a corrupt political system".