Phoenix was prompted to record an album after learning to play the guitar for his role as Johnny Cash in the 2005 film Walk The Line.
Los Angeles-based Burgess said: "Once he learned guitar, he found that he had quite a lot of demons inside himself that he wanted to expel through music."
The indie rocker added that he had been mixing the LP with his manager Alan McGee, the former head of label Creation Records, but Phoenix's attention to detail and perfectionism could prevent the album from ever seeing the light of day.
"All the tracks that me and Alan worked with him on were brilliant. But I think he just keeps scrapping everything or redoing everything. I'm sad to say that I think it's one of those records that may never come out, to be honest with you," said Burgess.
"It's an ongoing thing," he continued. "I'm trying to get Alan to force him to put it out at the moment, but I don't know [if he will]."