In the filing, prosecutors said they did not object to postponing an upcoming hearing as long as they can argue for access to the notebook on Tuesday, the new date for the hearing.
Holmes is charged with staging a meticulously planned assault on a movie theatre in the Denver suburb of Aurora in July. Twelve people were shot and killed and 70 were injured.
He faces more than 160 counts of murder and attempted murder. Prosecutors are seeking the death penalty.
Media reports have said the notebook contains drawings depicting violence.
It was found at the University of Colorado, Denver three days after the shootings. Holmes had been a neuroscience graduate student at the university, and the notebook was mailed to Dr. Lynne Fenton, a university psychiatrist who had been seeing Holmes.
The defence has resisted allowing prosecutors to see the notebook, saying it's protected by doctor-patient privilege.
If Holmes pleads not guilty by reason of insanity — as his lawyers say he wants to do — prosecutors are certain to argue that state law entitles them to see the notebook. Defendants who plead insanity are required to undergo a mental evaluation by state doctors and turn over some medical and mental health records to prosecutors.
Prosecutors probably believe the notebook has information indicating that Holmes was sane at the time of the shootings, said Karen Steinhauser, a former prosecutor who is now in private practice and teaches at the University of Denver law school.
"They probably believe it has some of the best and some of the most helpful information in regards to his mental state at the time he committed these acts," she said.
Judge Carlos A. Samour Jr. said he was inclined to allow the notebook to be raised at Tuesday's hearing but gave the defence until Friday to object.
The notebook is also at the centre of a legal battle over a leak to Jana Winter, a Fox News Channel reporter. Winter reported on the contents of the notebook in July, citing unnamed law-enforcement officials.
Defence lawyers contend that the leak violated a gag order, and they want Winter to identify her sources. The judge has not decided whether to order Winter to testify, saying he would wait to see if the notebook is entered as evidence.
Winter argues she should not have to identify her sources under Colorado and New York shield laws that allow reporters to keep the names of their sources confidential. If the judge orders her to reveal her sources and she refuses, she could be jailed.
Holmes was due in court Friday for a hearing in which the judge was expected to formally accept his plea of not guilty by reason of insanity. The judge postponed the hearing until Tuesday after the defence requested more time.
The prosecution and defence routinely decline to comment on the case, citing the gag order.
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