It's not 100% clear what your desired outcome is, but I can hazard some guesses.
1) If you're hoping that the specific position you were offered will be available in the future, then you need to lose that hope. Companies strive to fill positions as quickly as possible.
2) If you're hoping to work at the company in the future, then you're very close. The main difference is to avoid putting the onus on yourself to make contact in the future.
Thank you so much for your offer. I'm not looking to leave my current role right now, but would love to hear about future opportunities as they arise.
You show gratitude; you show that your "no" is about your current situation and not about their offer; you leave the door open for future opportunities; you leave it with them to re-initiate contact.
I believe this probably addresses your desired outcome of saying "No" without burning bridges.
I've been a hiring manager for the past 5 years and have been the recipient of communication from 100s of candidates. Good hiring managers understand the realities of the workplace and don't take polite rejections personally. On the contrary, a little courtesy will have at worst no impact on them and, more likely, a slightly positive impact that may pay off down the line.