The bid comes after a New York appeals court denied his effort to halt sentencing scheduled for Friday in New York state court in Manhattan.
In a filing released on Wednesday, Trump's lawyers asked the top US court to immediately order a stay in the case as he seeks an appeal to resolve questions of presidential immunity following an earlier Supreme Court ruling.
That appeal effort could reach the Supreme Court as well, his lawyers noted.Â
They also urged the court to issue a temporary "administrative stay" while it considers the request for a broader pause, the filing said.
Trump, who won another term in the White House and is set to take office on January 20, was convicted by a New York jury of covering up his former lawyer Michael Cohen's $US130,000 ($A209,000) payment to adult film actor Stormy Daniels for her silence before the 2016 election about a sexual encounter she says they had.
Trump has denied the encounter and any wrongdoing.
Steven Cheung, a spokesman for Trump, said in a statement his legal team had asked the Supreme Court "to correct the unjust actions by New York courts and stop the unlawful sentencing".
A spokesperson for Manhattan District Attorney Alvin Bragg, whose office brought the case, said prosecutors would respond in court papers.
The hush money case made Trump the first US president, sitting or former, to be charged with a crime and also the first to be convicted.
Since the verdict, his lawyers have made two unsuccessful attempts to have the case tossed.
In scheduling Trump's sentencing for Friday, Justice Juan Merchan last week said he was not inclined to sentence Trump to jail and would likely grant him unconditional discharge - which would place a judgment of guilt on Trump's record without any penalty such as custody, a fine or probation.
