keep an eye on, to
keep an eye on someone or somethingand have an eye on someone or something; keep one's eye(s) on someone or something; have one's eye on someone or something
Fig. to watch someone or something; to monitor someone or something closely. I have my eye on the apple tree. When the apples ripen, I'll harvest them. Please keep an eye on the baby. Will you please keep your eye on my house while I'm on vacation?
keep an eye on
1. To watch over attentively; mind.
2. To watch closely or carefully: keep your eye on the ball.