ONE EYE ON

{informal} Watching or minding (a person or thing) while doing something else; part of your attention on. - Used after "have", "keep", or "with". * /Jane had one eye on the baby as she ironed./ * /Bill kept one eye on his books and the other on the clock./ * /Chris tried to study with one eye on the TV set./ Compare: KEEP AN EYE ON.