keep one's eyes open

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.
See also: keep, open, someone
Farlex Dictionary of Idioms.

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.
See also: eye, keep, open
The American Heritage® Dictionary of Idioms by Christine Ammer.
See also:
  • keep (one's) eye(s) open (for someone or something)
  • keep eyes
  • keep eyes open
  • keep eye out
  • keep (one's) eye(s) out (for something or someone)
  • keep (one's) eye(s) peeled (for something or someone)
  • keep (one's) eye(s) skinned (for someone or something)
  • keep eyes peeled
  • keep (one's) eye out for (someone or something)
  • keep an eye out for (someone or something)