Feels like [Gym] Friends with [Client] Benefits

When I announced I would be starting my coaching practice two guys from my gym asked to be clients. They are amazing to work with and I feel completely comfortable during our coaching sessions. However, when I see them at the gym I feel completely awkward and self-conscious. I notice they don’t talk to me much either and we’re all just like pretending we don’t know each other but we do, but we don’t. I don’t have a problem getting into my workout but it’s in the in-between moments where people are chit-chatting that I freeze-up when they are near me. I want to act normal but I don’t know what that is because they don’t want anyone knowing they are my clients, and I’m nervous I’m going to blurt it out something like, “Talk to you at our next session!” Eeek! I’m also thinking it’s because they are guys that I’m getting self-conscious because we’re all in the same room, working out, watching.
C – Working out with Clients
T – They are watching me workout and judging me.
F – Self-Conscious
A – Fumble, Freeze, Say things I shouldn’t, overthinking what i do
R – I am judging myself

Do I want this to be my model?

C – Working out with Clients
T – We are here to work out and not judge each other. <–???
F – Comfortable
A – Focus on my workout
R – I am not judging myself or anyone else

I’m not feeling my intentional model is the right one yet, but I do know that I want to feel comfortable around my clients outside of our coaching sessions no matter where we are. I need some thought starters to get me there. Help. Thank you! 🙂