U.S. District Judge Donald Middlebrooks should not oversee the case because he was appointed in 1997 by then-President Bill Clinton, Trump said in a motion to disqualify the judge.
Bill Clinton has been married to Hillary Clinton, Trump's rival in the 2016 presidential election, since 1975.
Federal law states that judges shall disqualify themselves in any proceedings in which their impartiality might "reasonably be questioned."
Middlebrooks prejudice due to his connection to the Clintons is "so virulent or pervasive as to constitute bias against a party," the motion said, referring to a ruling in a previous case regarding such matters.
"The most important issue is not simply that justice must be done, but also that justice must appear to be done. This could not be more important in a case like the above styled cause, where wrongs in regard to a presidential election are to be redressed," it added.
It's not clear when the motion will be ruled on.
Middlebrooks' chambers did not pick up the phone or immediately return a voicemail.
Hillary Clinton does not yet have a lawyer listed on the court docket.
There has already been a recusal in the case.
Magistrate Judge Shaniek Maynard recused on March 25. She provided no explanation as to why.
The case was reassigned to Magistrate Judge Ryon McCabe.
Magistrate judges are appointed by other judges. They sometimes help district judges with cases.
Trump sued Hillary Clinton and approximately 30 other individuals and entities in March, alleging the creation of the dossier and its promotion committed crimes including conspiracy, theft of trade secrets, and obstruction of justice.