Jared – who is firmly in the spotlight thanks to his role in Oscar film Dallas Buyers Club - has been "hooking up" with Miley, reports US Weekly.
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The pair – who have known each other for a while – looked like they were getting on famously when they were snapped together last month at a pre-Grammys party.
Jared, 42, even posed with Miley's sister Brandi and mum Tish.
Sources say the pair are drawn together by their shared passions of music and art. And the fact they "both love to have a good time", apparently helps too.
Former Disney star Miley is well known for her successful music career, while Jared also has a legion of fans who follow his band 30 Seconds to Mars.
Miley with her ex fiancé Liam Hemsworth
Miley has been linked to a string of handsome young men since she split with Hunger Games star Liam Hemsworth. She was touted as the new love of Kellan Lutz when they were spotted leaving the same private jet in December, but the Twilight actor insists they are "just friends".
While she's yet to find lasting love, the 21-year-old singer says she is in a good place and has no regrets about her engagement to the Hunger Games star.
"I don't think I realised what 19 truly is, and I got engaged at 19, and I definitely wouldn't change being engaged. It was so fun wearing a fat rock for a few years," she said. "But now, I just feel like I can actually be happy."
Meanwhile, Jared broke off his engagement to Cameron Diaz in 2003 after four years with the actress.