My car is making a noise near the right front tire. It sounds like the noise a car makes when the power steering is low. But it is fine. I noticed a spot of grease on the driveway under the car, near this tire. Is there a place where grease should be?

Are the tires smooth or choppy as you look at the tread?
Run your hand along the tire tread,it should be smooth,no high or low spots.
High and low wear spots make a lot of noise on a tire.
Also,as you drive and hear the noise move the steering wheel slightly left and right,if you can change the noise at all then it may just be the wheel bearings.
Don't forget to make sure the metal inner dust shields beside the rotors are not touching anywhere on the rotors..

When you turn at low speed you most likely had your foot on the brake. As such, you are loading up the front suspension i.e. weight shifted to the front. Backing up at low speed has the same effect of loading up the front suspension. Your front tires contact patch to the pavement also increase in area -- think about the tire is less round but more flat surface touching the pavement.
In both cases (low speed/foot on the brake and backing up), they put more stress on the steering and thus the steering pump.

Hopeful fixes:
1) check tire pressure of both front wheels especially the sound occurred more often when turning left than right. The correct tire pressure when cold reduces the resistance from turning the steering wheel
2) check and/or replace steering pump belt(s). When they are worn out, they became inefficient in helping the steering pump to provide needed pressure to assist steering. Now the steering pump has to work 'harder' to provide the needed assistance to the steering

3) your steering pump is wearing out. Not totally dead yet. In cold days, the steering fluid is 'thick' --think viscosity. It is less efficient in circulate the pump. As such, a 'weak' pump has to work harder to make the thick fluid to circulate (to provide steering pressure). Mechanics refer to this cold days steering noise as "Morning Sickness". You can try to mitigate the problem by changing the steering fluid. You might need to change it a few times before the fluid in the entire system is purged and completely replaced.

Hopefully, inflating the tires to the correct cold temperate; changing the belts and/or complete steering fluid flush could solve your problem. They are all much less expensive than replacing the steering pump.

check the wheel bearings and drive shafts also does it do it on the same bit of road as the difference on road surfaces can make the tyres sound strange also get the pads on the breaks checked as well hope this helps ivan

sounds like the level is low, but check the alinement. might need pump

How long have you owned the car before discovering this noise? Have you replaced the tires recently? I'm not sure what your squeaking noise sounds like exactly, but it sounds like it could be one of the two problems. If it sounds kind of like rubber squealing your tires may be the wrong size for your car and at extreme steering degrees the tires can rub on the car in a number of places. If the squealing sounds more internal like a muffled tea kettle and you can feel it through your hands (even slightly) while holding the wheel it's probably your power steering. If your power steering fluid isn't low then you make want to get your power steering pump checked. This is always better than waiting until your power steering pump goes out on you while you are driving down the highway (usually happens in the middle of a curve). I can personally tell you that one is no fun at all! :)

Possible. If you have changed tires lately, make sure they put the right size tires on. If they went up in size by any measure, it could be rubbing on the tire well and thus making the noise. Check the users manual if you have it and check to make sure the tire sizes are correct. Also check your power steering fluid. That would make a humming or moaning noise but it would be noticeable while turning.

try it with the belts off you can start it and see if the spinning noise goes away then it's accessory's like bad alternator or power steering pump but dont run it more than a minute or two or it will start to overheat. and if it still makes spinning noise make sure it's not coming from the transmission /use a broomstick against the engine block near each piston to hear the condition of the pistons if there scored real bad it makes noticable diff noise than a diff piston will make. check the front of the engin the water pump sometimes needs to be replaced because the bearing in it drys up and fails / there sealed bearings in a water pump than go make noise . good luck give you stuff to think about.

the suspect part for a power steering whine is the power steering pump, flush (very important) the system and replace the PS pump..

That sounds like a left front wheel bearing gone bad My friend.. turning right transfers weight to the left side and it probably has a roar similar to a turbo fan jet.. Try it and lemmie know.. thank you

most probably a torn lower suspension arm rubber bush that would not show up if the car was on a 4 post hoist
there is a problem there as the noise would not be evident if there was nothing wrong
different tire pressures will give different noise when hit with a tire lever ( a trick used by truck drivers to check for flat/ under inflated tires
good tire solid sound
low pressure tire a dull sound