To eye up something is to look at it with interest or desire. Eye up the cakes, eye up a new car.
Of a person it is at best flirtatious and usually unwelcome, and of a thing it is harmless. It suggests wanting rather than merely noticing.
1phraseeye upTo look at something with interest or desire.
“He would eye up every bicycle in the shop window.”
eye up is a phrase.
Practised in Ways of Looking