That would only squeak when the suspension was bouncing though.

A dry CV or pot joint might make this kind of noise, but it's more likely to be a build up of crud somewhere.

Jack it up and give everything a darn good clean with brake cleaner to remove all the built up brake dust & rust and try it again..

Knuckle joint worn through the nylon cup

It would go away when you turn because the wheel and hub have a tiny bit of flex - enough to flex away from the dust shield. Not just a Mini phenomenon.

Thanks for the info I check that out today!  It was weird because it seemed to come out of nowhere and would only happen on a straight line.  Once I started to turn the sound would go away.  I appreciate the help!

I have seen /heard noise when a small rock got lodged between the shield and the disc. Same as Dan suggested. Take the wheel off and inspect the rear side of the disc and shield.

 Mini disk brakes have a dust/splash shield behind the disk. It is made of sheet metal and may be bent easily, making contact with the rotor. THe rotrs themselves do rust, especially on the outer rim. The rust can get quite flakey and expands as it grows. Eventually, the rust can come into contact with the dust shield, making the kind of noises you experience. When you took the wheel of and did your inspection and testing, you may have tweaked the dust shield, reducing contact, or dislodged some of the rust. Sometimes rust flacks can get between the rotor and the caliper body too.

Using a scraper or old flat screwdriver, you can scrape off some of the rust on the front and back surfaces of the rotor and around the outer edge. Do not tough the surfaces where the pads make contact. When you are satisfied, gently flex the dust shield as you turn the rotor to see if/where it makes contact and then bend it slightly away.

I was out for a drive and the front right side started squeaking and then turned into a grinding sound.  It didn’t stop when the car was out in neutral.  Didn’t intensify when the brakes were applied or let off.  It reminded me of a bad brake noise but I have no change in sound when I applied the brakes so it’s hard to say that’s why the problem is.  I took the wheel off to see if there were any obvious signs of rubbing and I didn’t see anything.  I rotated the axel when the car was up and didn’t hear anything.  When I put the wheel back on and test drove it the sound was much less then I was before.  Any ideas?  This is my first mini and I’m not exactly sure where to start.  The pads are good, the rotor has a small warp in it but nothing crazy.  I forgot to mention that the sound is not constant.  It is intermittent as the tire rotates.  Thanks in advance!!!