We don't say 'have an eye'. What you have written is a combination of two idioms: To keep an eye on something/somebody and To have your eye on something/somebody These have different meanings. Please tell us which idiom you want to ask about and we'll try to explain it. Remember that it is essential to use English idioms EXACTLY as you have heard or read them. Omitting or changing the smallest word can change the meaning or make them meaningless.

Having an eye on someone/something is used depending on the context. For instance a parent might say to a child "I have an eye (or my eye) on you" which means theyre watching them to see if they'll do something mischievous. In a different context but still similar, I might reassure someone "I have my eye on [them]", them being a person they care for and are worried about. And in a business context it might mean you're watching somebody to see how they progress. Having an eye on the new guy to see how much potential he has. Hope that helped!