According to Pat Yasinskas of ESPN, the Tampa Bay Buccaneers prefer Jameis Winston to Marcus Mariota at this point. In fact, according to Yasinskas, it could be the reason that the Bucs hired Dirk Koetter as their offensive coordinator over Marc Trestman:
I've heard that coach Lovie Smith prefers Winston over Oregon's Marcus Mariota. From what I have gathered, Smith chose Dirk Koetter as his offensive coordinator over Marc Trestman. The logic was simple. Although Smith and Trestman had similar philosophies about how to run an offense, they disagreed on the quarterbacks. Trestman preferred Mariota.
There is going to be a lot of debate over the two quarterbacks at the top of the draft with people having pretty strong feelings one way or the other. If they Titans aren't planning on taking a QB with the 2nd overall pick, which I don't believe they are, then the only thing that matters to them is that the Buccaneers take one or the other. That gives them the shot at the best defensive player on their board, who most believe will be Leonard Williams, or increases the value of the pick if they want to trade out.
As always, there is no guarantee that the information Yasinskas is correct. It could be someone in the Tampa Bay organization just throwing up a smokescreen for someone that really wants Winston to drive the price up for the #1 pick...or it could be 100% accurate. The world may never know.