The "Wrecking Ball" hitmaker, 26, and the 22-year-old Australian singer lay in bed watching old clips of the rock 'n' roll music legend, in a video shared on Cody's Instagram Stories.
In the short segment, Cody sweetly serenades Miley while they stream Elvis' performance of his song "Ku-Ui-Po". In the caption of the post, he shared the select lyric from the tune: "More today than yesterday."
The pair are rumoured to be dating since they were spotted kissing last week, following the "Slide Away" star's split from her husband of eight months, Liam Hemsworth, in August. Their PDA came after Miley's very public rebound romance with reality TV star Kaitlynn Carter, which ended after six weeks last month.
They have since been spotted together on several occasions, with Cody sharing a photo of him and Miley on his Instagram Story over the weekend, kissing her on the head with the caption: "Pre swim breakfast courtesy of baby."