The order was issued by the New York state tax department after Mr Cohen’s lawyer, Lanny Davis, said his client had information regarding the Trump Foundation, according to the anonymous official.
Barbara Underwood, New York Attorney General, filed a lawsuit against President Trump and three of his children, along with his foundation, in June.
She claimed President Trump had unlawfully used his charity as a personal “cheque book” to benefit himself.
The official is seeking to determine whether President Trump used money from his charity to contribute towards his 2016 presidential campaign.
Amy Spitalnick, spokeswoman for the attorney general, commented on the issue, saying: “We cannot comment on potential or ongoing investigations.
“As our lawsuit against the Trump Foundation illustrates, we will hold Donald Trump and his associates accountable for violations of state law, and will seek a criminal referral from the appropriate state agency as necessary.”
A spokesman for the Manhattan District Attorney Cyrus Vance declined to comment.
This comes after Michael Cohen pleaded guilty in federal court in Manhattan to eight charges on Tuesday.
The charges included tax evasion, bank fraud and campaign finance violations.
Mr Cohen’s lawyer, Mr Davis, stated his client possessed information that may be useful to the authorities in relation to the Trump Foundation investigation.
Mr Davis also said Mr Cohen had information relating to possible collusion between the Trump campaign and Russia during the 2016 presidential election.
Since winning the Presidency, there has been constant speculation surrounding whether the Trump campaign worked with the Russians to influence the outcome of the election.
Special Counsel Robert Mueller is continuing his investigation into possible collusion.
However, President Trump has constantly dubbed the investigation a “witch hunt”.
Andrew Cuomo, New York Governor, said Mr Davis had gone “out of his way to say Cohen would be forthcoming on both federal and state investigations”.
Concerns are also growing that President Trump may seek to shut down any criminal investigation by firing Robert Mueller or pardoning key witnesses.