Keep an eye on = keep eyes on留意

I gotta keep eyes on my son.我得经常留意我的儿子。

Keep an eye on 也有关注的意思

We will need to keep an eye on him! 我们关注一下他吧。

We’ll be keeping an eye on you.我们会关注你的。

You’d better keep an eye on your wife.你最好关注一下你妻子。