1
general::
Phrase(s): not breathe a word (about someone or something) [and] not breathe a word of it
Fig. to keep a secret about someone or something. • Don’t worry. I won’t breathe a word about this matter. • Please don’t breathe a word about Bob and his problems. • Don’t worry. I won’t breathe a word of it.
McGrawhill's American Idioms And Phrasal Verbs
2
general::
Not reveal a secret, keep concealed, as in You must promise not to breathe a word of what I'm about to tell you. This phrase relies on the verb breathe as meaning "to utter," a usage dating from the late 1500s.
American Heritage Idioms