Fan-like noise from left air vents area when accelerating

[MikeJM]

I've started noticing this weird noise from the left air vent area when pushing on the gas pedal.It feels like there's something like a leaf stuck somewhere that trembles when there's an air flow. I unmounted the air vent and checked if there's anything that might cause this and found nothing. I can't hear that noise in the left air vent area. So it's only noticed in the left side. I would suspect this was exhaust leak or belts/pulleys but I don't hear that noise when the car is parked no matter how high I rev the engine. I'll eventually take the car to a shop if I don't find the problem but just wanted to see if anyone else have had the same issue and got it figured out. Do you have any idea what else can cause this noise?