His relatives have filed a petition with the Tokyo District Court to have him moved from prison to a hospital.
Asahara, who has spent a decade in detention, mumbled unintelligibly and made unexplained gestures during his trial.
The sarin gas attack in 1995 killed 12 people and injured thousands more.
Asahara, whose real name is Chizuo Matsumoto, was sentenced to death in February 2004 after he was found guilty of 13 charges of murder and attempted murder.
He is appealing the verdict, but the trial has reportedly been stalled because his lawyer says it is impossible to communicate with him.
Eleven other Aum members have received death sentences, though none have been executed pending appeals.