It contained crude drawings of stick figures and descriptions of an upcoming attack, US news outlets say.
The University of Colorado, Denver, has confirmed that it received a suspicious package that it has handed to police.
James Holmes, 24, is being held over the massacre at the cinema in Aurora.
The reports emerged as the first funeral of the 12 victims was held.
Gordon Cowden, 51, was the oldest of those killed. His teenage children were also in the theatre during the shootings but emerged uninjured.
Fox News, citing an unnamed law enforcement source, was first to report that the suspect had allegedly posted the notebook.
According to the network, it contained “full details about how he was going to kill people, drawings of what he was going to do in it, and drawings and illustrations of the massacre”.
Other outlets also quoted unnamed sources as saying that James Holmes, who was preparing to quit his studies, had sent a package to the university.
But the college itself appeared to contradict media reports that the package had been sent before the massacre, and that it had remained unopened for days.
Officials at the university’s Anschutz Medical Campus said it had received a suspicious package on Monday that was immediately investigated and turned over to authorities within hours of its delivery.
The FBI refused to comment on the record about the reports, a day after a judge issued a gagging order limiting what officials can say about the case.
James Holmes was a neuroscience PhD student at the college until he took steps last month to leave the programme.
Many remain in hospital after the shootings, with several in critical condition.
Denver-area hospitals that are treating survivors said on Wednesday they would eliminate or limit medical bills for the casualties, some of whom had no medical insurance and faced huge costs.
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