keep an eye on
1. To watch carefully; not stop paying attention to.
Keep an eye on the stove in case the coffee boils.
You must keep your eye on the ball when you play tennis.
A good driver keeps his eye on the road.
The teacher had her eye on me because she thought I was cheating.
Billy keeps a jealous eye on his toys.
The lion tamer keeps a sharp eye on the lions when he is in the cage.
2. To watch and do what is needed for; mind.
Mother told Jane to keep an eye on the baby while she was in the store.
Mr. Brown told John to keep an eye on the store while he was out.
Syn.: TAKE CARE OF (1).
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Source: A Dictionary of American Idioms