Weird clunking sound in Reverse

I get an odd "clunking" sound from the front wheels only sometimes when I reverse and turn the wheel, like when backing in to a parking space. It doesn't happen all the time, maybe 50/50.

I have no idea what's causing the sound or how to even diagnose it...

 

Could be anything but no way for us to tell. Get 'er jacked up and start inspecting front end parts. Control arm bushings, ball joints, coilover mount bolts, tie rod ends, steering rack mounting bolts, slop in the steering intermediate shaft joint...

 

Loose lower control arm bolts.
Worn control arm bushings
Or ball joint.

Having experienced this same issue a few times. I'm going with loose LCA bolts.
Mine tend to do it after I have had an alignment. Those bolts like to be TIGHT.
You can't just get them "good and snug". They need to be tight.

 

What @TnShooter said, although another thing to look at is the brakes. After installing new pads several years ago, I had a clunk while reversing from the pads shifting. It eventually went away on its own, but I remember reading that some people have doubled up on the locking springs for the pads in order to prevent it.