keep (one's) eye(s) peeled (for someone or something)

To remain vigilant or carefully watchful (for something or someone). They should be arriving any minute, so keep your eyes peeled. Keep your eye peeled for a birthday gift we could give your mother. Tell everyone to keep their eyes peeled for the health inspector. We heard she'll be doing a surprise inspection someday soon.

keep (one's) eye(s) skinned (for someone or something)

To remain vigilant or carefully watchful (for someone or something). They should be arriving any minute, so keep your eyes skinned. Keep your eye skinned for a birthday gift we could give your mother. Tell everyone to keep their eyes skinned for the health inspector. We heard she'll be doing a surprise inspection someday soon.

keep your eyes peeled/skinned

Be particularly watchful; remain alert. This American expression dates from the mid-nineteenth century and presumably likens peeled or skinned to being wide open. An early reference in print occurs in J. S. Robb’s Squatter Life (1847): “Keep your eye skinned for Injuns.”