The 'Twilight Saga' actor – who recently called time on his relationship with co-star Kristen Stewart – was spotted with Elvis Presley's actress granddaughter at his Los Feliz, Los Angeles home over the weekend.
Riley – who was previously engaged to Alex Pettyfer – worked with Kristen on 2010's 'The Runaways'.
It was recently revealed Robert is writing songs to help get over his split from Kristen but is not planning to make them public.
A source said: "Rob's always had half a mind on his music, but when his film career and relationship with Kristen both took off at the same time, something else had to give.
"He's really enjoyed picking up his guitar again properly and it has given him something to focus on during the break-up. Everyone's saying that he's really talented, but he's adamant we'll only be seeing him in films for the time being."
The pair split for a second time after Kristen got back in touch with 'Snow White and the Huntsman' director Rupert Sanders, who she confessed to having an affair with last year behind Robert's back.
Robert's musical efforts have previously seen him record two tracks for the original 'Twilight' soundtrack, 'Never Think' and 'Let Me Sign'.
He has also previously said he originally wanted to be a musician rather than an actor.
He said: "I love the piano. I never really had any aspirations to be an actor when I was young. I wanted to play the piano in a bar, to be the old dude with a whiskey glass."