Wiktionary
keep an eye on
vb. (context idiomatic English) To watch and pay attention to.
WordNet
keep an eye on
v. follow with the eyes or the mind; "Keep an eye on the baby, please!"; "The world is watching Sarajevo"; "She followed the men with the binoculars" [syn: watch, observe, follow, watch over]
Usage examples of "keep an eye on".
I did what I could to find out who this guy was so I could keep an eye on him.