make eyes at (one)
To flirt with one by making suggestive eye contact. Is that girl making eyes at me, or am I just imagining it? You can't just make eyes at a person and expect them to come running—you have to talk to them and get to know them!
make ˈeyes at somebody
(informal) look at somebody in a way that tries to attract them sexually: He did nothing all evening but make eyes at the girls!