cast (one's) eye(s) on (someone or something)
To desire or covet someone or something, often greedily or selfishly. You better not cast your eyes on the last piece of cheesecake—I already claimed it!
cast your eyes on something
or cast your eye on something
If someone casts their eyes on or casts their eye on something or someone, they decide they want to have or own them. To our amazement, another developer has cast greedy eyes on the field next door.