The sides spent their ninth day before arbitrator Fredric Horowitz, who also heard the case from Sept. 30-Oct. 3 and Oct. 15-18. Rodriguez's legal team was set to call witnesses when the hearing resumed.
MLB and the players' association appear to be trying to finish testimony before Thanksgiving, and it remained unclear whether the New York Yankees third baseman would testify. He had been scheduled for an investigatory interview with MLB on Friday, but the session was canceled when Rodriguez's side said he was ill with flu-like systems and could not travel from California.
Rodriguez arrived at MLB's office on Monday morning.
MLB has been expected to assert that Rodriguez should not be allowed to testify at his grievance if he first refused to answer MLB's questions at the investigatory interview.
Rodriguez was suspended for 211 games by MLB on Aug. 5 for alleged violations of the sport's drug agreement and labor contract, and the players' association filed the grievance to overturn the penalty.
The three-time AL MVP said four years ago he used performance-enhancing drugs while with the Texas Rangers from 2001-03, but he has denied using them since.
A Florida police department said Monday it had reopened an investigation into the theft of documents related to baseball's inquiry.
Boca Raton police officer Sandra Boonenberg said the investigation was reopened several weeks ago based on new information stemming from Rodriguez's lawsuit against MLB, which accused the sport of engaging in a "witch hunt."
Boonenberg offered few details on the open investigation but said detectives have "a lot of leads that they're pursuing."
The documents were stolen in March from the car of Porter Fischer, who took them from Biogenesis of America, the now-closed Florida anti-aging clinic where he worked.
The clinic and its owner, Anthony Bosch, have been accused of providing banned performance-enhancing drugs to Rodriguez and other major leaguers. Bosch agreed to cooperate with baseball's investigators, and baseball later suspended 14 players.
Citing unidentified sources close to the investigation, ESPN reported last week that MLB impeded the Florida investigation.
"MLB investigators knowingly purchased stolen documents in their quest to allow Commissioner Selig to act, for the first time, as if he was tough on PED use in baseball despite striking a cooperation deal with Anthony Bosch who MLB knows is under federal investigation for providing steroids to minors," Jordan Siev, one of Rodriguez's lawyers, said in a statement.
MLB has repeatedly denied the accusation.
"The truth continues to be that we did not knowingly purchase stolen documents and there is an active police investigation to determine if the documents were in fact stolen," the commissioner's office said in a statement.