Did Marilyn Monroe want to perform as Medea, the character from Ancient Greek tragedy who murdered her children?

It’s certainly possible. She owned a copy of the play Medea as rewritten by poet Robinson Jeffers. In the play, Medea is married to the Greek hero Jason, who leaves her for a younger woman named Glauce. In doing so, he effectively abandons Medea and their children. Medea exacts her revenge upon Jason, first by murdering Glauce, then by murdering their children. Jeffers’ version, which had success on Broadway in the late 1940’s, deals with the themes of agency and inhumanism.
Marilyn Monroe’s copy of Medea was published in 1948, and while it is possible that she wanted to perform as Medea, I have another theory:
Marilyn Monroe based her performance of Nell in Don’t Bother to Knock on the character of Medea.
Nell in Don’t Bother to Knock is a troubled young woman who, at the climax of the film, attempts to murder the child she is babysitting. The movie is based on the novel Mischief by Charlotte Armstrong (you can read my comparison of the book and film here). Don’t Bother to Knock was released in 1952, only a few years after the success of Jeffers’ Medea on Broadway.

Often, when people look at Marilyn’s performance of Nell, they reference her own history with psychological issues and trauma (bother her own and her mother’s). Marilyn Monroe worked hard with her acting coach Natasha Lytess before her audition, and was given the serious role—impressing studio producer Daryl Zanuck who is quoted as saying she only should play “sex pot” roles.
While Marilyn Monroe possibly based her performance of Nell on her own experiences, there are similarities between the characters of Medea and Nell. Not only are both willing to kill children to attain their goals, but there is an even broader theme of being trapped. Medea is trapped by fate, while Nell is trapped by responsibility. The anger and evil that arise in both characters comes from being trapped and trying to have individual agency.
So, did Marilyn Monroe want to play Medea? Possibly—and if she had, she certainly would have done a superb job. But arguably, in some ways, Marilyn Monroe did play Medea—channeled through her performance of the character of Nell.