"With the information we have right now, we haven't taken him off of our list right now," Smith said.
Smith said the Bucs have not yet met with Winston, but intend to meet with him at the combine, as will most other clubs.
The quarterback-needy club has been linked to Winston since he applied for early entry into the draft. The Heisman Trophy winner has done plenty on the field to warrant consideration for the No. 1 overall pick, but scouts and analysts have significant concerns over a series of off-the-field incidents during his time with Florida State.
Winston was investigated for an alleged sexual assault but did not face criminal charges and was cleared in a Florida State code of conduct hearing stemming from the December 2012 incident.
"As far as how we look at it, if a player has been accused of something, and again, they've been exonerated of it, you have to go with it," Smith said. "That's what our justice system is all about. That's how we'll go forward."
NFL Media Insider Ian Rapoport reported Wednesday during NFL Network's coverage of the combine that Smith and Bucs GM Jason Licht have done "more than their share" of research into Winston's history of off-field incidents.
"They've delved into all of those details and they are not close to being finished on digging into Jameis Winston and Marcus Mariota either, by the way," Rapoport said.
Rapoport said the Bucs will visit the schools of top prospects, go through on-field workouts with them away from the Bucs' facility and also bring players to the team facility for a visit before making a decision.
Three NFL Media analysts believe the Bucs will pick Winston with the first pick, according to recent mock drafts. He is considered to be the most pro-ready signal-caller available to teams due to his size, anticipation and arm strength, among other traits.
While Smith's comments might indicate a willingness to take Winston, he didn't shut the door on drafting Mariota. Smith said he likes what he sees from the Oregon product as well.
Either way, it's clear that Smith wants everyone to know that Winston is under consideration for the Bucs at No. 1.