i just need to discover how to do that in a subtle way...
So your question isn't at all isn't if he is interested in you, but how you can subtly let him know you are interested in him.
Is that correct?
Otherwise you're going about it bass ackwards coming her to find out if some person has interest in you, and putting the onus on him to do something about it.
It's not so much how to "discover" how to do this, it's not uncovering some unknown artifact. You want to figure out how to let him know you have interest.
This is a whole different story.
You can pussyfoot around making yourself miserable and anxious trying to discover some way without actually doing anything, or by gazing back soulfully into his eyes hoping he takes the hint, or you can take some action.
At the end of a session, when you are about to leave, simply ask him if he'd like to go get a cup of coffee with you sometime. That's as subtle as it's going to get.
If there's a non answer, or a no, you've got your answer as to his interest. By the next time you see him, he'll have forgotten all about it. In his business he gets questions like this all the time, so don't worry about it.
Even if it's a non answer (or even a no) you may have just caught him by surprise, and now he's aware of your interest, and at a later time might take you up on it.
He's just a human, just like you. A guy. That's all. It's not like he's got some super awareness of the universe going on, or some edge on you.
"Would you like to go for coffee sometime?"