Winston is considered one of the top prospects in this draft class, but Smith has faced questions about Winston's off-field issues.
Winston was accused of sexually assaulting a former Florida State female student in December 2012. Authorities did not file charges, and Winston was also cleared in a university Code of Conduct hearing.
In addition, Winston was cited for stealing crab legs from a grocery store in Tallahassee and was assessed a one-game suspension after he was seen shouting an obscene phrase in the Florida State student union.
Over two seasons as the Seminoles' starting quarterback, Winston completed 66 percent of his passes for 7,964 yards with 65 touchdowns and 28 interceptions. He won the Heisman Trophy in 2013 and posted a 26-1 record.
"I'm very comfortable with Jameis, if we decide to go in that direction," Smith said, according to Schefter.