Robert O'Ryan told a judge he wanted to enter the insanity plea during a hearing Monday in Los Angeles.
The 36-year-old is scheduled to go on trial Tuesday on felony burglary and stalking charges.
He is accused of going to a studio where Johnson was performing on "Dancing With the Stars" in an attempt to meet the gymnast.
Authorities say they found two guns and love letters to Johnson in O'Ryan's car.
He could face nearly four years in state prison if convicted. The judge warned O'Ryan that if he is found to be insane, he could be confined to a state mental hospital for much longer.
