Kelly Osbourne 's departure opened the floodgates ... Hollywood agents are scrambling to get their clients a shot at her " Fashion Police " seat -- but they'll have to get past Kathy Griffin first.

Our sources at the network say it's been inundated by candidates -- pitched mostly by agents from CAA and WME. We're also told E! execs are squashing Kathy's desire to apply the stamp of approval. They say the final choice will be theirs.