- Aaron Hernandez's trial date could be firmed up Monday
- Prosecutors OK with him transferring to different jail
- Hernandez's defense wants medical records from New England Patriots
(CNN) -- Ex-New England Patriot Aaron Hernandez has two separate scheduled court appearances this week, taking on his former team and challenging a search warrant in the murder investigation of Odin Lloyd.
On Monday, a judge may firm up a trial date in Lloyd's death, now penciled in for October. Hernandez has pleaded not guilty both in the June 2013 shooting of Lloyd, and in a separate Boston case, the drive-by double slaying of Safiro Furtado and Daniel Abreu. That trial is already set for May 2015.
While he waits for trial, Hernandez wants to move to a new jail.
Since his arrest in June 2013, Hernandez has been held at the Bristol House of Corrections in a 10-feet-by-7-feet cell.
Inside the case against Aaron Hernandez
Former New England Patriots tight end Aaron Hernandez is led into the courtroom to be arraigned on homicide charges on Wednesday, May 28, in Boston. Hernandez pleaded not guilty in the 2012 killings of Daniel de Abreu and Safiro Furtado. He has also been charged in the 2013 death of semipro football player Odin Lloyd. 
At a press conference on May 15, Suffolk County District Attorney Dan Conley announces that Hernandez has been indicted for the July 2012 killings of de Abreu and Furtado and charged with three counts of armed assault with attempt to murder. Prosecutors allege Hernandez killed de Abreu and Furtado after de Abreu bumped into Hernandez at a nightclub, causing him to spill his drink. 
Hernandez is brought into the Attleboro, Massachusetts, District Court for his arraignment on June 26, 2013. He was charged with first-degree murder in Lloyd's death. Hernandez was release by the Patriots less than two hours after his arrest. 
Hernandez answers questions during Media Day on January 31, 2012, before Super Bowl XLVI against the New York Giants in Indianapolis. 
Hernandez carries the ball as the Patriots play the Cincinnati Bengals in Foxborough, Massachusetts, on September 10, 2010. 
Hernandez looks up after being tackled during a game against the Philadelphia Eagles on November 27, 2011, in Philadelphia. 
Tattoos on Hernandez's arm are visible during the pregame warmup on December 4, 2011. 
Hernandez scores a touchdown against the Buffalo Bills on January 1, 2012, in Foxborough, Massachusetts. 
Hernandez catches a pass against Chase Blackburn and Aaron Ross of the New York Giants during Super Bowl XLVI on February 5, 2012, in Indianapolis. 
Hernandez runs for a 12-yard touchdown past Deon Grant of the New York Giants in the third quarter of Super Bowl XLVI on February 5, 2012, in Indianapolis. 
Hernandez celebrates his touchdown in the third quarter of Super Bowl XLVI. 
Hernandez, center, reacts during the SEC Championship game between the Florida Gators and the Alabama Crimson Tide on December 6, 2008. The Gators went on to win the national title. 
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Photos: Rise and fall of Aaron Hernandez 
What jail is like for Aaron Hernandez His legal team is asking a judge to transfer him closer to their Boston offices to make their commute shorter. A judge is expected to rule on that request Monday.
In court documents, prosecutors aren't objecting to the move, but they are objecting to other defense accusations that the Bristol sheriff who runs the jail has "collaborated... in an effort to generate evidence to be used against Hernandez."
The defense also complains that they are assigned to a specific visitation room and unable to have private conversations with Hernandez.
Sheriff Thomas Hodgson and prosecutors deny they've done anything wrong.
On Wednesday, in a second court appearance this week, Hernandez's defense team hopes to get a court-approved subpoena to demand the New England Patriots turn over all medical records and psychological tests involving their former star tight end.
A motion calls the records potential evidence that may bear upon Hernandez's state of mind and "physical and mental state" prior to Lloyd's murder.
The move indicates his attorneys might be considering a diminished capacity defense -- being less capable of knowing right from wrong -- legal experts said, if there is credible evidence.
"My instinct is they try to argue he wasn't mentally capable of planning or intending any murder, and thus, first degree murder should be off the table," University of New Hampshire law professor Michael McCann told CNN.
Hernandez also is waiting for a ruling on another defense motion to throw out the murder charge, arguing the state has failed to meet minimum standards called probable cause to make that charge stick.
In a June hearing, his lawyer Jamie Sultan told a judge all he's heard is "a lot of smoke" but few specifics.
"Who killed Mr. Lloyd? Why? Whether it was part of a plan and if so, whose plan? What happened to the car, and what happened at the scene?" Sultan argued in that hearing.
The defense is also trying to quash a June 18, 2013, search warrant executed at Hernandez' home. Along with cellphones, an iPad and other items, the search turned up evidence including surveillance video from interior cameras.
The images include a still allegedly taken shortly after Lloyd's slaying that shows Hernandez holding what prosecutors believe is the murder weapon, according to a law enforcement source. A .45-caliber gun allegedly used to fire eight shots has never been found.
The case against Hernandez: Where's the weapon?
Defense attorneys argue investigators did not have the legally required search warrant paperwork with them.
In a motion, Hernandez' lawyers state a Massachusetts state trooper entering the house "clearly has no file folder in his hand," with documents.
If the defense successfully quashes the search warrant, the pictures from that search could become inadmissible.
Prosecutors maintain the search was carried out by the book.
The rise and fall of Hernandez
Source: Hernandez's anger over two trivial incidents linked to killing
CNN's Michelle Rozsa and Laura Dolan contributed to this report.
