We got "The Real Housewives of New York" star at ABC Studios in NYC and our photog asked her about rumors Joe slept over at her house after they got super flirty on Andy Cohen's show.

Luann says they went out to have drinks after the taping and there was great chemistry between them ... but he didn't spend the night and they're not hooking up.

It's not that Luann doesn't want to sink her cougar claws into Joe ... she says the "Southern Hospitality" hunk has a girlfriend, "Summer House" star Danielle Olivera.

Luann's respecting whatever Joe and Danielle have going on ... though he's recently said they aren't official. Danielle was in the audience at Andy's show while Luann and Joe were getting flirty on camera.

But, if Joe comes back to Luann as a very single man ... she's going to pounce at the opportunity.

After all, Luann tells us she considers herself a bit of a cougar.