Elba, 42, has given the album the working title Murder Loves John.
"I'd like to dissect the idea of someone who has to deal with so much darkness," he told John Wilson on BBC Radio 4's Front Row.
Next week the actor releases his debut album, mi Mandela - inspired by Elba's African heritage and his role as Nelson Mandela in 2013's Long Walk to Freedom.
It is intended as the first of a series of albums which are character-inspired.
Elba said: "Detectives carry a lot of stuff. They meet someone who's done something heinous, but they have to have an objective perspective on them until proven."
"That could create some really good songs... and definitely an interesting mood, musically," he added.
The "character albums" are not Elba's first foray into the music world. The Wire actor released a five-song EP called High Class Problems Vol 1 in 2010, under the moniker Driis. He released an earlier EP - Big Man - in 2006.
He told Wilson he believed David Bowie would be a significant influence on the album.
"Luther listens to Bowie. He likes Bowie. John loves the idea that David's music is escapism for a complex mind."
"I'm not saying that I am going to make an album that sounds like a Bowie album. I'm just saying that would be an inspiration for some of the writing and songs."
Elba is due to return to the role of the troubled police detective in a two-part Luther special for broadcast next year.
He added he hoped to perform on stage in the near future and is in talks over a possible musical role.
Idris Elba appears on BBC Radio 4's Front Row on Wednesday 26 November, at 19:15 GMT.
Idris Elba is planning to release an album of music inspired by his BBC detective character Luther.