The 25-year-old actor previously recorded two tracks, Never Think and Let Me Sign for the original Twilight soundtrack.
Sources say the sound of the album will be "organic" and use traditional instruments.
The friend added: "The album Rob will make will be guitar based and drums, very organic-sounding, nothing pop. Like stripped-down Ray LaMontagne meets Van Morrison."
Robert's Twilight co-star, Jackson Rathbone, has previously praised his ability as a guitarist.
He told how Robert "loves to play the blues. He can hold his own on a guitar. We enjoyed jamming together when we had the time. Very humble and quiet guy."
Robert has also said he loves playing piano, and as a child hoped he could make a living from it.
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."