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general::
Phrase(s): keep an eye on someone or something [and] 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?
McGrawhill's American Idioms And Phrasal Verbs