The Arizona Republic's Nick Piecoro gives us three relief names on the D'Backs' radar, now that LaTroy Hawkins is off the board: J.J. Putz, Bob Howry, and Brendan Donnelly. The D'Backs already added Aaron Heilman on November 19th.
Putz will reportedly throw for teams tomorrow; he's got the White Sox, Cubs, Nationals, Pirates, and Tigers as other known suitors. We haven't heard much on Howry and Donnelly yet. I think Donnelly is a possible sleeper, as outlined in this October discussion post.
The Diamondbacks can certainly expand their search beyond those three righty relievers - we outlined the free agent market here and trade market here.