Court records show the hearings have been held over the last few weeks behind closed doors but neither prosecutors nor defense lawyers have revealed the purpose of the sessions.
Bill Miller, a spokesman for the U.S. Attorney's office that is handling the case, declined to comment Friday.
Several media organizations, including The Associated Press, are petitioning to open the proceedings. The next hearing takes place on February 7 in D.C. Superior Court.
Ingmar Guandique, an illegal immigrant from El Salvador, was convicted in 2010 of killing Levy, whose remains were found in 2002 in a heavily wooded area of Washington's Rock Creek Park.
Prosecutors acknowledged at the outset of the case that they had no physical evidence linking Guandique to Levy's death, but they argued at trial that the attack on Levy fit a pattern of attacks by Guandique on other female joggers in Rock Creek park around the same time she went missing. Their case also leaned heavily on the testimony of a former cellmate of Guandique, who claimed that Guandique admitted while behind bars to killing Levy.
Guandique is currently serving a 60-year prison sentence.
The case captured the nation's attention because of Levy's relationship with California congressman Gary Condit. Though Condit, who is no longer in Congress, was interviewed by investigators, authorities eventually ruled him out as a suspect and don't believe he had anything to do with her death. Condit testified at trial that he had no role in Levy's disappearance or death, but evaded questions about his relationship with her.
Levy's father, Robert Levy, told KGO-TV in San Francisco that he has not been told what's going on. He said Guandique was a "convicted rapist and an illegal alien."
But, he added, "if he's innocent of murder, he shouldn't be in jail for it."