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The Rays traded right-hander Nathan Karns to the Mariners in November.
Rosenthal notes the team also could move Alex Cobb, who will miss much of 2016 while recovering from Tommy John surgery. But that seems a sell-low scenario the Rays likely wouldn't consider.
The 26-year-old Smyly and 25-year-old Odorizzi are under club control until 2019 and '20, respectively, while Moore's five-year contract extension with three escalating club options ends after the '19 season.
Boxberger, who posted 41 saves in 2015, is under club control through 2019, while McGee (2.07 ERA last two seasons) can become a free agent in '18.
Cash Kruth is a reporter for MLB.com. Follow him on Twitter at @cashkruth. This story was not subject to the approval of Major League Baseball or its clubs.