make eyes at

I saw you making eyes at that woman earlier. Why don't you ask her for a date before it's too late?

 If you 'make eyes at someone' you look at them in such a way that shows you are sexually attracted to them.

make eyes at
（人）に色目を使う

make calf eyes at
〔少年や少女が〕幼稚な恋心で異性を崇拝的に見る

make goo-goo eyes at
～に色目を使う

Tom often makes goo-goo eyes at me during class. 
 トムは授業中によく私に色目を使う。

make sheep's eyes at
（人）に色目を使う