In their most recent Developer Livestream, Blizzard has confirmed that after overwhelming PTR feedback, players will be able to see Greater Item Affixes on dropped gear – before even picking it up!
Diablo Season 4 Developer Livestream Summary
Items with one Greater Affix will have one star, while items with two will have two stars, and so on. Additionally, items with Greater Affixes now display the new icon in the tooltip: