The two were pictured together at the Stagecoach Festival in Indio, California over the weekend, and though there's speculation the two are romantically linked, multiple sources tell PEOPLE it's strictly platonic.
"They just met backstage at Stagecoach," a source close to the country star tells PEOPLE. "They're new friends and enjoyed hanging out last weekend. She's a fan of his music."
Osbourne documented the meeting by posting a photo with 30-year-old Lynch backstage, seemingly toasting with mini shot glasses.
"Thank you Dustin & everyone on your team for treating me like family!" The 7D star, 31, captioned the image.
And family let each other borrow their duds – in her next Instagram, Osbourne shared a selfie sitting in traffic, wearing what looked to be Lynch's "Stay Country" hat.
On Friday, the star was in great spirits while celebrating her pal Shaun Ross's birthday at SBE's new hotspot Doheny Room.
Reporting by MELODY CHIU and SARAH MICHAUD