The 30-year-old pitched for the D-backs from 2006-08 before filing for free agency in November. He appeared in 141 games for the team, including 15 as a starter and compiled a 15-7 record.
Cruz, who was 4-0 with a 2.61 ERA last year for the D-backs, is classified as a Type A free agent, which means that any team that signs him will need to give the D-backs their first-round pick in the 2009 First-Year Player Draft.
It's been speculated that the Draft compensation issue has caused teams to shy away from signing Cruz, who made a little more than $1.9 million last year. It's possible that the D-backs could use some of the money budgeted for the first-round and supplemental pick they were going to get for Cruz to instead re-sign him.
Both D-backs general manager Josh Byrnes and Cruz's agent, Barry Praver, declined comment.
Steve Gilbert is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.