From Longman Dictionary of Contemporary Englishhave/keep your eye on somebodyhave/keep your eye on somebodyWATCHto carefully watch everything that someone does, especially because you do not trust them We want Taylor in jail where we can keep an eye on him. → eye
Examples from the Corpus
have/keep your eye on somebody• His face had grown serious, and he kept his eyes on the road.• He kept his eyes on Ezra, surveying him.• He kept his eyes on his father, who had betrayed him.• As I told you, I have my eyes on a very different sort of market.• I kept my eyes on it the whole time, he wrote.• Mulcahey kept his eyes on the circles that widened out from the pebbles he dropped into the water.• We have to keep our eyes on the sandy path.• It was not only Percy Makepeace who kept his eyes on Hilary. 