have one’s eye on+人或物，表示的含义却大不相同，请看：
一、
have one’s eye on sb
1
密切注视；盯住；监视
to be watching sb carefully, especially to check that they do not do anything wrong
I don't like you attitude, I've got my eye on you.
我不喜欢你的态度，我盯上你了。
2
看中；看上 ；注意
to be thinking about asking sb out, offering sb a job, etc. because you think they are attractive, good at their job, etc.
He's got his eye on the new girl in your class.
他看中了你们班上新来的那个女孩。
You should be careful; I think Danny's got her eye on your boyfriend. 你应该小心点，我觉得丹妮对你男朋友有意思。
Ever since we got to this party, that man's had his eye on you. 我们一到这个派对，那个男的就一直在注意你。
二、
have one’s eye on sth
想得到；想买到
to be thinking about buying sth
Neil's had his eye on those shoes for a while. We should buy them for his birthday. 尼尔已经看中那双鞋子好一阵子了。我们应该买给他当作生日礼物。
How's your diet going? You've had your eye on the cake display all lunchtime! 你节食得怎么样了？吃中饭的时候你的眼睛一直盯着那个蛋糕陈列架
Mark has his eye on the captaincy of the basketball team. 马克一心想当那支篮球队的队长。
另外，see sth with half an eye 一眼看出，一目了然，一看即知，
Obviously anyone can see with half an eye that the nature of this picture is trying to depict an asleep person/individual.
显然，任何人都能一看即知这幅画的本质是在刻画一个睡着的人。