Constant Drainage Sound in Wall

We have a constant sound of "gurgling" water in the wall behind our toilet. It never seems to vary much although occasionally it is louder. I have crawled under the house twice and there is no apparent leaking water and a check of the water meter shows no active leaks (watching the small red triangle on the meter, which does move when water is running in the house). I've checked the water heater to see if the line connected to the pressure release valve could be draining, but can't hear anything and the pipe is cold. I have been up on the roof and listened to the top of the vent lines over our bathrooms and can hear water running in the pipe. I have had a plumber out and he doesn't know what the problem is. We also cut off the valve to our outside sprinkler line to eliminate water in that line from being a consideration.
Question - Could a trap between the house and the city sewer line have failed, creating a conduit for sound from the city sewer line draining to be heard under the house? We are at a loss for where this sound is coming from.

I don't think that you have a trap between your house and the main line...numerous traps within the house, basically at every sink, toilet, etc. Do you have any obvious bubbling in the toilet? If it is really windy, sometimes you can hear things through the vent, but I've not heard gurgling or water running. I'm not a pro...my thoughts.

Have you lifted the lid of the toilet tank to check the ballcock (fill valve)?

I'm with The Pipe Rat on this. The first suspect for constant water running is the toilet. If the flapper is leaking, you would have the drainage sound, but occasionally would also hear the fill valve operate. But if the fill valve has a slow leak, you may not notice that sound, but it would cause a constant trickle to overflow the toilet weir and drizzle down the pipes.

I thought of the toilets as well, but have turned off the water to each one and completely drained the tank, and you can still hear the running water sound. I also don't have any movement of the small red triangle on the water meter that should indicate any low level flows. I'm at a loss at this point.

You say gurgling sound? My first thoughts after the water closet has been eliminated is a stopped up drain. But this shouldn't be a constant noise. Now i can agree if you listened through the roof vent you could easily hear running water from the main but I wouldn't interpret that as a gurgling noise. Stumped at this point maybe more info would help. Leaning away from a water leak though. Shut your water off at the meter and see what happens. Then update us as to the results. Good Luck

We have turned the water off at the meter and at the meter for the sprinkler system and there is no ongoing leak registering on the meter. When you turn the water on, the small red triangle on the meter spins, so the meter is working. Bottom line is no water leak, but we still have a constant water drainage noise behind the bathroom wall.
HELP!

What kind of heating system do you have? Could it be from that?