They've made an offer to infielder Ramon Vazquez for one year and a club option, but that was weeks ago and it does not seem like the two sides were close financially.
Vazquez's agent, Melvin Roman, said he had received an offer that was better than the D-backs' offer from another club and that his client was looking for a two-year deal.
"We're still waiting to hear back," Roman said.
Chances are they might be waiting for a while as the D-backs let the market sort itself out a bit and see if Vazquez's price comes down.
The D-backs have also talked with free agents Mark Loretta and Damion Easley, who could serve as the right-handed part of a platoon with Vazquez at second. The club has explored the possibility of trading for the Cardinals' Adam Kennedy, but his $4 million contract for next year might prove problematic.
"We'll just keep working at it and see what happens," Byrnes said.
After having parted with top prospects in deals over the past couple of years, the D-backs do not have the system depth to pull off the kind of trade they did when they shipped six Minor Leaguers to the A's for Haren last winter.
"We are not as set up to make a major move as we were last year," Byrnes said.
Teams will no doubt ask about young pitchers Max Scherzer and Jarrod Parker and continue to be told that the two are off limits.
Backup catcher Miguel Montero could be available in the right deal, but in the limited talks the D-backs have had with teams about him, they could not find the right match.
Arizona would like to move outfielder Eric Byrnes and/or infielder Chad Tracy, but finding potential suitors could be difficult because of either health or contract issues.
There will be other news coming out of the Meetings regarding the National Baseball Hall of Fame.
The Veterans' Committee ballots will be announced on Monday at 11 a.m. MST. Tuesday, the Ford C. Frick Award winner will be announced, while on Wednesday the Spink Award winner will be revealed.
Also on Wednesday, Major League Baseball will have an announcement regarding the 2009 World Baseball Classic, and on Thursday the Rule 5 Draft will be held as the Meetings conclude.