It would be the first major revival of a Miller play since the dramatist's death three years ago.
All My Sons, to be directed by British-born Simon McBurney, would also allow Holmes to be more than "Mrs Tom Cruise" for six nights a week.
The actress has committed to taking part in a private workshop of the play in May. She will play the part of a woman who visits her former neighbours, the family of a missing pilot she once loved.
Producer Eric Falkenstein has already cast Broadway veterans John Lithgow and Dianne Wiest, which has had the desired effect of making Ms Holmes more comfortable about taking on her first play since high school.
Holmes has told McBurney and Falkenstein that she is serious about working in the theatre.
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