Greene will not be on the Rangers' roster to begin the season, Jeff Wilson of RangersToday.com reports.
Greene missed several days of Cactus League action due to a broken fingernail, but he still managed to pitch 5.1 spring innings, surrendering two earned runs with a 6:2 K:BB. Greene will presumably exercise the opt-out clause in his contract, but the 35-year-old likely won't receive more than a minor-league deal elsewhere.