The younger Biden's lawyers in a filing in US District Court in Delaware cited public reporting suggesting "incessant, improper, and partisan pressure" applied by Trump to then-Attorney General William Barr and senior Justice Department officials Richard Donoghue and Jeffrey Rosen to investigate Biden.
Barr declined to comment.
Rosen, Donoghue and a representative for Trump did not immediately respond to a request for comment.
Hunter Biden, 53, in October pleaded not guilty to charges that he lied about his drug use while buying a handgun, in the first-ever criminal prosecution of a sitting US president's child.
Special Counsel David Weiss brought the charges against Hunter Biden after a proposed plea deal unravelled under questioning from a judge.
The president's son has been the subject of relentless criticism from Trump and Republican lawmakers, who have set his foreign business dealings at the centre of an impeachment inquiry into Joe Biden by Republicans in the US House of Representatives.
The White House argues the impeachment probe is politically motivated and unsubstantiated by evidence of wrongdoing by the president.
Hunter Biden's lawyers argued in their court filing that political pressure by Trump during his administration tainted the investigation.
The filing cities instances in which Trump reportedly raised the Hunter Biden investigation with Justice Department officials, including conversations where Trump was reportedly rebuffed.
In his memoir, Barr wrote that he told Trump in an October 2020 conversation that he would not discuss the younger Biden.
Hunter Biden's lawyers are seeking the documents by December 1, arguing that may be relevant to pre-trial legal motions he plans to file.
