Gregerson, for whatever reason, has not been right for weeks now.
Harris has been terrific (hard to fault him for giving up a barely-over-the-fence solo shot to Bautista today), but do you risk spoiling a good thing by burdening him with Closer expectations so soon? Plus, he's more like 92 with the FB, so not a traditional "Closer arsenal". There's also the clubhouse chemistry angle - replacing a high-paid vet like Gregerson with a kind of out-of-nowhere guy like Harris might not go over too well.
Fields has the Closer-grade heater, but has had a couple rough outings himself lately, and based on how sparingly the team uses him, I wonder if he could hold up to a Closer's usage. They seem to be afraid of him breaking.
I don't think anyone wants to see Qualls closing right now.
Neshek has been great but again, is he Closer material? Ditto Sipp, especially being a lefty.
Out-of-the-box/desperation ideas include Feliz, Vincent Velasquez, and Appel at AA.
Or they can just ride it out with Luke G and hope he can fix things.