At a hearing Friday, prosecutors told D.C. Superior Court Judge Geoffrey Alprin that they have provided the bulk of evidence in the case against Ingmar Guandique.
Levy disappeared in May 2001 and her remains were found a year later in Rock Creek Park.
Defense attorneys say they still need to conduct interviews with at least 10 other people they described as possible suspects. They asked the judge to push back the January trial date, but Alprin refused.
Alprin set another status hearing for October.
Levy was romantically linked to former U.S. Rep. Gary Condit. Authorities questioned the California Democrat in Levy's disappearance, but he was never a suspect.