Lawyers for Mr Trump filed an emergency application with the Supreme Court on Tuesday asking the court to issue a stay or suspension of a grand jury subpoena demanding the tax returns from his accountants.
The move comes as Mr Trump’s third nomination for the Supreme Court, Amy Coney Barrett, is going through her confirmation hearing.
Ms Barrett was nominated to fill the vacancy created by the death of Justice Ruth Bader Ginsburg in September.
Mr Trump is also planning on formally asking the Supreme Court to hear his appeal on the lower court ruling, which is related to an ongoing criminal investigation into the Trump Organisation by Cyrus Vance Jr’s office.
In their filing Mr Trump’s lawyers say “there is reasonable probability” that the Supreme Court will hear the appeal.
In July the justices voted to reject Mr Trump’s first argument that he should not turn them over but said he could argue the case in lower courts.
Following that Mr Trump’s arguments have been rejected by federal district and appellate courts in New York.
The district attorney’s office wants the financial records from Mazars USA as part of an investigation into how hush money paid to two women who claimed to have had sex with the president was accounted for by his business.
Prosecutors have also suggested that Mr Trump may be facing a criminal tax probe.
Last month a New York Times investigation claimed that Mr Trump only paid $750 in federal income tax in 2016 and 2017 and no federal income taxes in other years.
The newspaper also claimed that Mr Trump faces personal debt repayments of more than $400m.
Mr Trump has said he will not release any tax returns while they are being audited by the IRS, even though there is no restriction on him doing so.