I carry a sling that sits on my right hip, similar height to a fanny. I just put a small carabineer on a loop fairly high on the back strap on my pack. Take an appropriate length of paracord (I need just a couple inches) from the end of the net and put another smaller carabineer on the other end of the paracord. Connect carabineer to carabineer. I like it so it rides high enough so it’s out of the way and it’s not hitting my legs when I walk, but not so high that it’s tough to reach around and grab.
In your case, I would just add a couple of inches of paracord to the end of the net with a carabineer attached. Carabineer the net right to the strap on your fanny pack somehow. Probably behind you, or off to the side on your weak arm side so line doesn’t catch on it while casting.
And not a weird question at all. I don’t like carrying nets, and generally don’t while fishing small, wild Trout streams. For 99% of the fish you catch on those streams, you don’t need one, and the net is more often a hindrance and in the way than help. I recently caught a spritely 14” Brown on such a stream and wished I had one though…it happens. If I’m fishing a larger stream, with generally larger fish, and I’ll be in the stream channel most of the time and not brush busting and climbing over stuff, I regularly carry a net as described above though.