Doug Martin wants to be paid like DeMarco Murray in the 2016 free agency period, which for the Buccaneers, is a little too rich for their taste. Tampa Bay is also not looking to replace Martin with any of the running backs on its roster, so it could be possible that it's looking to replace him with either a free agent running back, or a draft prospect.
Martin may not have a lot of leverage with the Buccaneers, as they can probably find a younger and just as productive running back in the draft, so there is no need for them overpay him. They may also look to sign a free agent as a placeholder or permanent replacement for him.
It's hard to believe that Tampa Bay would spend its ninth overall pick on a running back, and not for more protection for quarterback Jameis Winston. The Buccaneers do, however, have around $48 million in cap space, so finding a free agent running back shouldn't prove that difficult. They don't necessarily have a bigger free agent than Martin, so if he goes, they could potentially use a lot of cap space in fortifying their offensive line and rebuilding their running game.
Backup Charles Sims is a solid passing-down back, but not a very effective every-down back, so the Buccaneers will most likely try multiple new options at the position. Chris Ivory, Lamar Miller, or Alfred Morris and/or a rookie running back could make suitable replacements for Martin.