keep eye on
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keep one's eye on someone or somethingand have one's eye on someone or something
Fig. to have one's attention directed to someone or something. Please keep your eye on the children while I go to the store. Bill kept an eye on his expenses because he was spending too much money.
keep your/an eye on something/somebody
to watch or look after something or someone Could you keep an eye on the baby for me a while? I kept my eye on him all the time as I felt sure he was about to do something stupid.