According to Rosenthal, the Diamondbacks are looking for a "top-of-the-rotation-starter" and like Shields, whom they tried to trade for two years ago. Shields is ranked No. 3 in SI.com writer Ben Reiter's Top 50 free agents.
If Arizona were to sign Shields, it would need to clear payroll space, which Rosenthal said could potentially be "impossible."
Marlins general manager Dan Jennings was the Tampa Bay Rays scouting director when Tampa Bay drafted Shields in the 16th round in 2000. Signing Shields would cost Miami the No. 12 draft pick in 2015, according to Rosenthal.
Marlins beat reporter Joe Frisaro reported in October that Shields would likely be on top of the list of players Miami would target over the offseason.
Shields went 14-8 for the Kansas City Royals in 2014 with a 3.21 ERA and 180 strikeouts in 227 innings. The nine-year veteran has a career 3.72 ERA.
- Molly Geary