The 36-year-old Davis, a left-hander who strung together four consecutive seasons of double-digit wins from 2004-07, went 1-7 with a 6.50 ERA last year for the Cubs. He has four seasons with at least 200 innings pitched, but his career hasn't been the same since he was diagnosed with thyroid cancer in 2008 and underwent surgery.
"Seriously?" manager Don Mattingly asked when told that Davis was among the hopefuls.
Another athlete trying out was Minnesota Vikings defensive back Jarrad Page, which came as a shock to the Vikings. Page played college baseball at UCLA and was drafted three times by MLB teams as a center fielder without ever signing.