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.

The 24-year-old twisted an ankle in the warm-up and damaged a knee during her second-round defeat by American Alison Riske on Court 18.
Mladenovic said both players wanted to stop after only two games "in case something bad happened".
The All England Club said the courts were as "playable as per normal".
Temperatures have reached 30C at Wimbledon, with around 60 people treated by the St John Ambulance for heat-related symptoms on Thursday.
The Met Office is predicting highs of 26C on Friday and 23C on Saturday, but with more cloud cover on both days.
Mladenovic blamed the weather for making the courts too dry.
She said: "The colour of the court, the fact that there's no more grass, the fact that the baseline where we are running, it's very slippery. There's no grass.
"You kind of have to run light and be careful, not to push or press too much, too hard, which is strange to play on."
Mladenovic, who lost 2-6 6-4 6-4, added: "It's quite unique with your opponent, after two games, you both agree on stopping playing in a Slam.
"I'm just honestly very happy and blessed that I didn't injure myself that much."
An All England Club statement read: "The court preparation has been to exactly the same meticulous standard as in previous years.
"Grass is a natural surface and it is usual for the baselines to start to be showing signs of wear and tear four days into the Championships."
Idris Elba is planning to release an album of music inspired by his BBC detective character Luther.
[NEXT_CONCEPT]
France's 12th seed Kristina Mladenovic complained about a "damaged" court at Wimbledon, claiming poor surfaces are the talk of the players' locker room.