It's very unlikely that the Indians will non-tender an arbitration-eligible player today. I wouldn't be surprised, though, if they do non-tender one of the marginal pitchers on the 40-man roster and re-sign them to a minor-league deal. Brian Tallet, Jose Diaz, and Jason Stanford seem likely candidates for this tactic.
I'll update this post as interesting players (to me) are non-tendered. Some names to keep an eye on: Hee Seop Choi, Wade Miller, and Craig Wilson.
Update [2005-12-20 23:5:47 by Ryan]:
Some interesting non-tenders thus far: RHP Wade Miller (injury), RHP Chad Bradford, RHP Dan Kolb, OF Jamal Strong
Update [2005-12-21 11:2:33 by Ryan]:
The Indians' only non-tender was RHP Jose Diaz. Other interesting non-tenders: OF Eric Byrnes, RHP Grant Balfour (injury), RHP Joe Borowski, 2B Junior Spivey. Craig Wilson and Hee Seop Choi were tendered contracts.