Miley is right. None of the yarns out there is absorbent enough.
But! Here's a handy-dandy tip that you don't usually find in stores: Take a regular kitchen-tea-type towel. Fold down the top 1/4. Across the fold, maybe using a crochet hook, pick up a row of stitches. Knit these stitches, decreasing at the beginning and end, in your favorite knitting stitch. When you get to about 5-8 stitches remaining, work even for about 6" or so. Make a buttonhole. Work another 1/2" then bind off.
Sew a button at the base of your long tab, where you stopped decreasing.
Now you have a wonderful handy towel that you can loop over the fridge doorhandle. Presto! One easy-to-find towel! And it can be washed whenever you like.