Kyle Richards Says She's Not Single, Mum on Relationship with Morgan Wade

Kyle Richards is trying to set the record straight on her love life ... she says she's not single but is mum on rumors about her relationship with country music star Morgan Wade.

The 'RHOBH' star was gassing up her Range Rover in L.A. Friday when a paparazzo asked her about her relationship status.

Kyle says she's not living the single life. She says she's "very good friends" with Morgan, but would not address the buzz about the 2 in the wake of her separation from husband Mauricio Umansky.

There are lots of social media photos of Kyle and Morgan together ... Kyle's clearly a fan of Morgan's music, offering up her favorite song.

Kyle and Mauricio are calling BS on rumors they're divorcing after 27 years of marriage.

Kyle and Mauricio spent the Fourth of July together Tuesday ... posing for photos with his arm around her.