keep (one's) eye(s) open (for someone or something)
To remain vigilant or carefully watchful (for something or someone). They should be arriving any minute, so keep your eyes open. Keep your eye open for a birthday gift we could give your mother. Tell everyone to keep their eyes open for the health inspector. We heard she'll be doing a surprise inspection someday soon.
keep one's eyes open
Also, keep one's eyes peeled or skinned . Be watchful and observant. For example, We should keep our eyes open for a change in the wind's direction, or Keep your eyes peeled for the teacher. The first phrase dates from the late 1800s; the second and third, both colloquial and alluding to the lids not covering the eyes, date from the mid-1800s and 1830s, respectively.