na-adjective
Describes a look or manner that shows strong desire for something, often with a nuance of envy or wistfulness. Commonly used as 物欲しげな目 or 物欲しげに見る.
彼はケーキを物欲しげに見つめていた。
He was staring at the cake with greedy eyes.
子犬が物欲しげな
The puppy is waiting for a treat with a longing face.
欲張り is a noun/adjectival noun meaning 'greedy person' or 'greediness' in a general sense, while 物欲しげ specifically describes an outward appearance or manner of wanting something.
羨ましげ focuses on envy, whereas 物欲しげ emphasizes a visible desire for an object or thing.
Compound of 物 (もの, 'thing') + 欲し (ほし, stem of 欲しい 'want') + げ (suffix indicating appearance or manner). The exact historical derivation is uncertain, but the components transparently combine to mean 'looking like one wants something'.