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Phrase(s): keep one’s eyes open (for someone or something) [and] keep one’s eyes peeled (for someone or something)
Fig. to remain alert and watchful for someone or something. (The entry with peeled is informal. Peel refers to moving the eyelids back. See also keep an eye out (for someone or something).) • I’m keeping my eyes open for a sale on winter coats. • Please keep your eyes peeled for Mary. She’s due to arrive here any time. • Okay. I’ll keep my eyes open.
McGrawhill's American Idioms And Phrasal Verbs