Castro, 53, is accused of imprisoning and brutalizing the three women in his home for about a decade. He has pleaded not guilty to 977 charges including 512 counts of kidnapping and 446 counts of rape.
He is also accused of aggravated murder for beating and starving one of the women to force her to miscarry, a charge which could carry the death penalty.
Gina DeJesus, 23, Michelle Knight, 32, and Amanda Berry, 27 were freed from Castro's home in a rundown area of Cleveland on May 6, along with a 6-year-old girl Castro fathered with Berry during captivity.
At a hearing on Wednesday, Cuyahoga County Judge Michael Russo asked lawyers for both sides if they were still working toward a possible plea agreement to resolve the case. They replied yes.
Cuyahoga County Prosecutor Tim McGinty said he was ready to go to trial as scheduled on August 5 but lawyers for Castro protested that they would not have enough time to review the evidence against their client.
"How are we supposed to defend this gentleman?" Castro's lawyer Craig Weintraub asked.
Defense lawyers left the court on Wednesday without speaking to reporters, but they have repeatedly said they would like to reach a plea agreement to avoid trial.
Legal experts have said an agreement would avoid putting the three women through the ordeal of testifying to the horrors they allegedly faced during years of confinement.
Michael Benza, former prosecutor and senior lecturer at Case Western Reserve University School of Law, said both sides are "posturing" in the Castro case.
"It (the early trial date) could create a real legal problem for the prosecution. They have to turn over certain evidence to the defense and if it goes to trial without the evidence a conviction can be overturned," Benza said.
Ohio Attorney General, Mike DeWine said the state had tested and turned over 110 pieces of evidence to prosecutors in the case, and are expecting to hand over 62 more items this week.
Of the 110 pieces of evidence turned over, 99 were tested for DNA, 10 for latent prints and 11 underwent firearms-related testing, according to DeWine.
DeWine said all testing essential to the case will be done by August 5.
"This is a priority for this office," DeWine told reporters. "We are paying overtime to get it done."
County prosecutors could still bring another indictment against Castro that includes the death penalty.