We caught up with Kyle at LAX Wednesday ... and, we had to ask her about the wild story that she attempted to hook up with the "Yellowstone" star while at her vacation home in Aspen.

Richards says there's zero truth to the rumor ... claiming she's only met KC two times -- and spoke with him for about a minute total.

KR says Sutton Stracke -- her 'Real Housewives' costar who dropped the bombshell news on the 'RHOBH After Show' -- must've been making a joke when she said the two stars did the deed ... 'cause she doesn't have that kind of relationship with Costner.

Richards admits Costner's a good-looking dude -- and, she's a big "Yellowstone" fan -- but, that's as far as her affection for Kevin goes.

As we've told you, Kyle and her longtime husband Mauricio Umansky separated last year ... and, Kyle's spent quite a bit of time with country singer Morgan Wade -- leading many to believe the two might be an item, though Kyle's repeatedly denied it.

Kevin went through his own breakup last year ... splitting from his wife of more than two decades, Christine Baumgartner. His divorce got downright contentious at times -- and, resulted in Costner needing to pay big money to Christine.