I'm a photographer and when I started out, I remember randomly approaching guys who worked at the A&F store to model for me. I have my business card in hand and prepared a script. "Hi, my name is Ronald and I'm learning photography. I really think you have a great face and body. I was wondering, if you'd consider modeling for me. Here is my business card. Thank you and goodbye."
I did that twice, before discovering an easier approach via ModelMayhem.com.
The point I was making is that, I think—you should summon up the courage and talk to the person at the gym!
"Hey! You're [Instagram Handle]. I really admire your physique and would you mind sharing me your nutrition supplements or food prep?"
How is this situation any different from running into a celebrity dressed incognito? If you're fan of the celebrity, you'd be using your excited voice and expression matching the surprised enthusiasm. You'd quietly approach him/her, trying not to make a scene and offer compliments to him/her.
The only situation, where I would consider inappropriate or creepy is when you perform your introduction inside of the locker room or near the showers.