What could be causing a slight thumping noise coming from the tires/wheels/area? on 2003 BMW Z4

At low speed I noticed a slight thumping noise coming from the tire/wheel/suspension area. Upon acceleration, the noise is less discernable.

Asked by for the 2003 BMW Z4
Z3s and Z4s are known for strut/shock mounts which would make the noise you're describing
1 more answer
This sounds familiar. Following a quite detailed assessment by two different mechanics at my shop (which I trust), the conclusion was that the slight knocking sound I'd been hearing was actually most likely coming from the transmission and was most likely benign, especially if it doesn't get louder over time. The Getrag transission is supposed to be quite bulletproof. The most probably explanation (from the shop's senior technician, with 25 years experience, much of it with BMW) was that the sound was due to play between the gears themselves (being moved by the residual effect of the driveshaft still spinning), since the sound disappears under load. In other words, coming to a stop in neutral or with the clutch pedal depressed there is the slight knocking sound, but with the transmission engaged and under load (either accelerating or decelerating) the sound is not apparent.

Hope this is helpful. I've decided not to worry, as long as the sound does not change or get worse (and so far, after 3,000 miles with the car, it hasn't)...