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Public defenders for James Holmes, 25, said in the Arapahoe County District Court filing that prosecutors have so far not accepted the offer, which would spare their client the death penalty in one of the deadliest mass shootings in US history.
Holmes faces multiple counts of first-degree murder and attempted murder stemming from the July 20 massacre at a showing of the Batman film "The Dark Knight Rises" in Aurora, Colorado that also wounded 58 people.
Arapahoe County District Attorney George Brauchler has said that he would formally inform the court during a hearing scheduled for Monday whether his office would seek the death penalty against Holmes.
Brauchler has not made his decision public, but in February announced that he had added a death penalty lawyer to the prosecution team.
All three of Colorado's death row inmates were convicted and sentenced in Arapahoe County. At a state legislative hearing earlier in March, Brauchler testified in favour of keeping the death penalty on the books in Colorado.
A spokeswoman for the Arapahoe County District Attorney's Office could not be reached for comment on Wednesday afternoon.
"Prior to arraignment, Mr. Holmes made an offer to the prosecution to resolve the case by pleading guilty and spending the rest of his life in prison without the opportunity for parole," lawyers for Holmes say in the papers.
Holmes was arraigned on March 12. At that hearing, Arapahoe County District Judge William Sylvester entered a not guilty plea on his behalf after defense attorneys said they were not prepared to enter a plea.
In today's pleading, defence lawyers said that if prosecutors agree to take the death penalty off the table for Holmes the case could be resolved at Monday's hearing.
Attorneys for the former University of Colorado neuroscience graduate student, who surrendered to officers outside the theatre minutes after the shooting rampage, had been expected to mount an insanity defense on his behalf at trial.
"As previously stated in court, counsel for Mr. Holmes are still exploring a mental health defence, and counsel will vigorously present and argue any and all appropriate defences at a trial or sentencing proceeding as necessary," defense lawyers said in the court papers.
"Nevertheless, Mr. Holmes is currently willing to resolve the case to bring the proceedings to a speedy and definite conclusion for all involved," the defense said.
Lawyers for Holmes have said in court filings that their client has been hospitalised twice since his arrest, once after hitting his head against a cell wall.
Holmes was also held in restraints for several days at a psychiatric hospital in November after jail officials determined he was a threat to himself, according to his defence team.