Citing their client's worsening health, attorneys for Scarsdale native Robert Durst will ask a Los Angeles judge on Monday to declare a mistrial.
They will argue that 78-year-old Durst is too sick to testify, depriving a jury of hearing his side of the story.
Durst is on trial for the 2000 shooting of his close friend Susan Berman.
Authorities say Durst allegedly killed Berman because she had information on what happened to Durst's wife Kathie.
Kathie has been missing since 1982, since Durst said he dropped her off at the Katonah train station, so she could return to their Manhattan apartment.
In May, the Westchester District Attorney's Cold Case unit began taking another look into what happened to Kathie.