The Bears, who hired GM Ryan Pace and head coach John Fox this off-season, will have met with the draft's top two quarterback prospects in Winston and Marcus Mariota.
Pre-draft speculation has placed both Winston and Mariota as top-five selections, while Chicago will pick seventh. The Bears return quarterbacks Jay Cutler and Jimmy Clausen from last season's team that finished 5-11.
Winston, 21, passed for 3,907 yards and 25 touchdowns at Florida State last season.
The NFL draft begins April 30.
- Jeremy Woo