My whirlpool dryer is making a terrible squeaking noise. What could be possibly causing this?

Here are some ideas.

1. Roller bearings failed or is failing.
2. Bearing in motor has failed or is failing.
3. Bearing in idler pulley has failed or is failing.
4. Belt sliding and squeaking on drum or belt sliding in pulley.

Here's where you can find manuals for the dryer:

http://shared.whirlpoolcorp.com/product_literature/search.jsp

There's no service manual listed, but there is an owners manual and a parts list. The owner's manual has a (trivial) trouble-shooting section that you should look at first. It's not likely to help, but it needs to be done so you can say that you checked it out.

I looked for a service manual without any luck. You can try these links for a "basic service manual": http://www.davesrepair.com/pdfmanuals/km27indrymanual.htm or http://www.applianceaid.com/partsmanual.html

The diagram shows a couple of "support rollers". I would think they might be at fault. You'll have to remove the drum to get at them. For that matter, you'll have to remove the drum to get at almost anything.