Some names and notes of players that have been floating throughout the interwebs:

Braden Looper - Rotoworld seems to think the Reds would have an interest in his services.  Not sure if there is any real rumor here.  Sounds like speculation:

Braden Looper (Cardinals) - Looper's 4.94 ERA and dismal strikeout rate in his first year as a starter suggested that he'd have a hard time lasting another season in the rotation in 2008, but he was able to improve for the Cardinals, finishing 12-14 with a 4.16 ERA. That's enough to insert him into the Jason Marquis class of starters and potentially land him another three-year deal as a free agent. The top teams probably won't be after him, but clubs looking for a guy to eat innings could see considerable value in his durability. It'd be for the best if he stays in the NL.

Previous prediction: Nationals - three years, $21 million
New prediction: Reds - three years, $21 million

Jocketty has signed Looper in the past, so it's not out of the realm of possibility, but I see this one as highly suspect, especially at that amount.

Miguel Montero - This one comes courtesy of the East Valley Tribune (via Redszone):

As the Diamondbacks conduct their due diligence this offseason, they have found significant interest in reserve catcher Miguel Montero.

"That’s a pretty popular name," a major league source said.

While the D-Backs would prefer to keep Montero because of his offensive productivity and his affordability, his marketability seems to make him the most likely trading piece to address their hole at second base.
. . . . . . .

Boston could be in the market for a catcher if free agent Jason Varitek goes elsewhere, and Detroit, Cincinnati, Houston and perhaps Milwaukee also might have interest.

Montero put up solid numbers in the minors: .291/.356/.467, though those could be a bit inflated by the Pacific Coast League.  He's 25 years old and doesn't go into arbitration until after next season, so he's still cheap.  I'm not sure the Reds are a match if the Dbacks are looking for a 2B, but he's an interesting catching option, especially since he'd set up a nice Lefty-Righty platoon with Hanigan.

Oliver Perez and Jon Garland - Rotoworld seems to think the Reds really need to sign some pitching, I guess.  The writer is much more non-committal on this one for the Reds as he only mentions them as possible players on these two guys.  I don't have a whole lot of interest in Garland, unless he is desperate and wants to sign a one-year deal.  I've always liked Perez, butBoras has been arguing that he's one of the top 5 lefties in the game and that his career path looks a lot like Randy Johnson and Sandy Koufax.  Translation: he'll be expensive.  So, no thanks for that kind of money.

Jermaine Dye - Ken Rosenthal mentions in his latest column that:

The Reds are looking for right-handed power, and general manager Walt Jocketty told the Cincinnati Enquirer that he spoke with the Rockies about Matt Holliday. The Reds also inquired about the Marlins' Josh Willingham before he was traded to the Nationals, and remain interested in Atkins.

MLB Trade Rumors speculates that Jermaine Dye might be a nice fit.  The White Sox brass is currently in Arizona evaluating talent (I'm assuming that doesn't mean they are at the strip clubs).  As Thundering Turtle points out, these players are currently in the AFL: Carlos Fisher, Robert Manuel, Pedro Viola, Sean Watson, Justin Turner, Chris Valaika and Drew Stubbs.

I don't think Dye makes sense for the Reds.  He's the kind of player that you pick up to fill that last remaining hole.  At 35, he's not the type of player that build with.  The Reds should be looking for those types of players.