Thumping noise and steering wheel shakeMany things can cause a car to make those weird sounds.
Worn suspension joints - jack the car up so the wheel is off the ground (you’ll need to do this for all 4 corners) and shake the tyre from top to bottom and from side to side (with someone holding the steering wheel on the front) there should be no play in either direction. Any play in 1 direction will usually require a joint to be replaced, if there’s play in both directions then the wheel bearing may be at fault. If theres play only up and down its the strut top mount - to find this one you have to shake the suspension strut it self up and down with the wheel off the ground - so you may need to remove the wheel to check this one.
Now with the car jacked up on that side with the wheel about 2 inches off the ground use a steel bar under the wheel and lever the wheel up and down slightly, you should be able to look at the end of the axle and see if the suspension arm is moving up and down separately to the axle.If so replace the bush.
To feel if there's a worn strut top bearing then lightly hold the spring by hand and have your assistant move the steering from left to right with the wheel on the ground - a worn bearing will feel 'notchy' through the spring. The wheel needs to be on the ground for the test to load up the bearing.
Worn drive shaft joint - typically these won't produce any vibration unless badly damaged but they can be noisy or 'clonk' for a long time beforehand, turn the steering to full lock and look at the drive-shaft rubber boot there should be no rips or tears in it and the suspension should be clean and dry of any grease. If you reverse at a reasonable speed with the steering on full lock a worn joint will 'click'.
Worn mountings - check the tightness of the engine and gearbox mounts and their condition - this is best done by using a jack to take the weight of the engine off the mounts and seeing if any cracks or splits open up in the rubber.Also check the tightness of the mounts bolts.
Rotate The Tyres Manually And Check
If the noise changes with rotating the tyre then yes I'd agree the tyre is possibly worn off centre
if you look closely at the edges of the tread blocks on the outside of the tyre you will probably see they are scrubbed on one edge
so if the strut mount is worn its possible the castor or camber of the wheel is incorrect and so scrubbing the tyre
If you can't find any slack in the suspension I'd suggest taking the car for a 4 wheel alignment to reset the suspension geometry.
This Will Help.