Hi fellas, i have this question eating me alive.Listening to jazz is not the same as listening to rock or some type of electrónic music.We cant Just listen to Art Tatum or Oscar Peterson as background noise.So this question will appeal to jazz heads. How to really listen to jazz and how to get the must out of any jazz style (swing, cool jazz,bebop,dixieland etc).I m not an expert but i always try to really get whats going on when a pianist plays…Things like chromatic passings,playing inside and outside,i pay attention to prahse repetitions and fragments of the melody during a jazz piano solo, licks and blues licks,scales like the blues scale and the melodic scale and finally call and response play…Just making some examples. I m going to drop a vídeo i was listening today as a bait to throw some ideas feel free to share your opinion and knowledge. 
https://youtu.be/IZERfh28Od0
I think it’s not the style of music but the ACT of listening that you reference, But once in a while I surprise myself by actually hearing and noticing a tri tone or some other music interval — when I am NOT actively listening, like in the car… like my brain still makes these connections on my behalf I’m always amazed that I noticed it, because I’m not strong at all in theory.
Yes different level of listening … but neither think its about the style of music.
“Jazz” is even very used as background listening in our life ( dinner 
, elevators , phones 
,…) where nobody even take care about what they hear. The different levels of listening is more an intellectual act of analysis with different interest about music .
Hayden talked of that recently : talking and i hear that lot ( all master musicians talk about this) about just taking only one song and taking care of listening deeply each instrument and for soloing musicians like pianists its the same just taking one element (bass line, melody line , rhythm patterns, runs …) .
Fred Hersch says he can listen hours long just one song of an artist he loves, and says theres no other way to get deeply in the song and in the artist style… taking time time time. Some zen attitude. But different levels of understanding music makes different levels of listening too.
And secondly the way we listen can be directed on what we want to work on ; like runs , time feel , arranging melody,… no end
But maybe a live analysis 
of a song of our master Hayden (or Jovino, Tuomo, Lyndon… ) could be a very interesting point 
.
We can talk a lot about , but the only things is doing it ourself , no other way . But guidance makes things easier for sure.
PS our style of life with thousand of cd avaible where ever we are, makes this even more harder and rare, very easy to lost focus on things. and take time for it… but as musicians and music lovers 
we try to keep this in our practice 
.
Interesting question @Ivan.
I agree that there is many different ‘levels’ to listening.
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The ‘first level’ would listening in the background whilst cooking, or driving for example, and your hearing the music, but not really following along. This is still very worthwhile listening and this is why we should be doing this all the time.
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The next level would be listening along to a tune you know, and feeling where you are in the form. If it’s a tune I know, I always try to follow along with the form when I’m listening. For example if I’m listening to a 12 bar blues, my ears always pickup on the turnaround in the last 2 bars. This can be from the distinctive pattern that the bass players walks, or perhaps the subtle flick of the drums that the drummer does to indicate the form is starting again. There’s many little cues like this that you can be listening out for.
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The next level would be listening and working out the notes and rhythms. I do this whilst sat at the piano with my Bose Speaker hooked up to my laptop, and I often use programs like Transcribe, but the more I do this I’m sometimes able to transcribe directly from Spotify or YouTube without the need to loop or slow down. However, this does depend on how fast/complex the recording is… I would find it hard to transcribe some of Tatum’s right hand runs without slowing it down
It’s worth noting that slowing down the record seemed to be essential when I first started transcribing, I’m slowly getting better this, and I’m often able to work out the notes and rhythms at the original speed of the recording which is liberating.
If I like a record, I will listen to it very regularly for days or even weeks, and then I attempt to transcribe from it. That’s very important in my opinion. Spend some time to listen and absorb what’s going on, perhaps counting through the form and identifying what you like. That way when you sit down to transcribe, you know exactly what you are doing. Compare it to arriving at the gym with your workout all mapped out 
For me, the beauty of listening and transcription is that it allows you to take your sound in the direction you want to take it.
If you like the sound of something, listen to it repeatedly, transcribe it, study it, and then play around with it to make it your own.
I like the quote/idea:
Every time that you listen and transcribe from a recording, you are making a ‘musical investment’ for the future. It might be months or years before those sounds show up in your improvisation but everything you listen to will eventually manifest itself into your style of playing.