Winston, a redshirt sophomore, has only played two seasons with the Seminoles, but is being projected as a first-round pick in the 2015 draft. Florida State coach Jimbo Fisher recently said he "wouldn't be shocked either way" regarding whether Winston turns pro after this season.
Vick is currently the Jets' backup but was once considered one of the most dynamic quarterbacks in the league. The No. 1 overall pick in the 2001 draft was renowned for his athleticism and ability to evade defenders in the open field.
However, Vick's career has been clouded by off-field controversy. He spent 18 months in prison for operating a dogfighting ring. Winston has dealt with several off-field incidents, including a sexual assault allegation and a citation for stealing crab legs from a grocery store.
"I think he's a great player," Vick said. "I've been around so long, I appreciate guys coming out of college. I look forward to watching him. I have high expectations for him. I think he, over time, has made some poor decisions. Have I been there to know exactly what happened? No.
"But I do know one thing: He may make some poor decisions, but he gets on that football field and he plays his ass off. Yeah, he can mature. He'll mature. I see him maturing as time goes on. Like, this year hasn't been as bad of a year as the first year was for Jameis. I think the kid will continue to improve. I think he's the future of the NFL."
Florida State has yet to lose a game with Winston as its starting quarterback.
The 6-foot-4, 230-pounder led the Seminoles to a 14-0 record last season, including a win over Auburn in the national championship, and has helped them to a 13-0 mark this season. Florida State will take on Oregon in the Rose Bowl -- one of two semifinals in the College Football Playoff -- on New Year's Day.
Even though Winston's statistics have dipped and scouts have raised concerns about his performance, Winston is still regarded as one of the top quarterback prospects in the nation. In his latest mock draft, SI.com's Chris Burke projects the Jets to select Winston with the No. 6 overall pick.