The Post reports the Manhattan DA is scrutinising whether the value of Trump Organisation properties were manipulated to defraud banks, insurance companies or tax authorities.
After subpoenaing records from Trump's accounting firm Mazars in August 2019, Vance wrangled with Trump's lawyers for their client's financial records up to the Supreme Court of the United States, twice.
Mr Vance or the district attorney's office have not spoken about the grand jury proceedings, which are kept secret.
The grand jury will be looking into the matters where Trump has been accused of paying hush women to tackle his hidden sexual relationships with women also his improper relations with lenders.
The inquiry had fought to get hold of Mr Trump's tax records and more recently has appeared to focus on the Trump Organization's long-time finance chief, Allen Weisselberg.
"No other President in history has had to put up with what I have had to", raged Trump, who described the investigations as "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".