either a cabin vent fan or some other fan that runs all the time.
Since noises are notoriously hard to pinpoint I'd hazard a guess the noise is coming from one of the radiator fans. You can I think check this out by starting the engine and upon hearing the noise determine if the A/C is on. If it is then turn it off and stop the cabin vent fan. If the noise goes away well there you are.
If the noise doesn't go away the noise is coming from some other source. I do not think the engine compartment vent fan runs all the time. If it does then that's a candidate source for the noise.
Another possible source for the noise would be the cabin fan that runs to circulate air over an inside temperature sensor. In my car there is supposed to be a small fan behind the circular grill on the dash over on the passenger side of the car. This fan circulates cabin air over the temperature sensor to keep close tabs on the cabin air temperature so the climate control system can keep the cabin temperature at the desired setting temperature.
There is another possible explanation, way out there though, and that is there is a relay acting up. Once in awhile, my 996 makes a rapid clicking noise when I turn on the key and start the engine. The noise is clearly present though before I even turn the key from on to start. The clicking doesn't last long, under a minute (and probably under a half a minute) though the duration seems longer than that.
I mentioned this to a tech and he offered the idea it was coming from a relay. Nothing's failed yet and the noise is not present all the time and I have not found a need to have this diagnosed.