White has plenty on his plate after being limited to just five games due to injuries since being selected with the seventh overall pick of the 2015 NFL Draft.
"We're not gonna harp on anything that happens -- a dropped ball, a route run the wrong way, a wrong split, a missed assignment," Nagy said, via the Chicago Sun-Times. "We don't harp on any of that with any of the players -- and in particular with him.
"We just want him to be him and play -- play fast. And he's done that so far. Again, it's going to be up to him to do it in the preseason games and see where it takes him."
White, who has yet to catch a regular-season pass from Bears quarterback Mitchell Trubisky, has 21 receptions for 193 yards and no touchdowns during his career in Chicago.
The 6-foot-3, 216-pound White sustained an injury to his left leg and didn't play at all as a rookie, and suffered an injury to the same leg that limited him to four games in 2016. Last season, he started the season opener but sustained a broken left shoulder blade in the game that knocked him out for the rest of the year.
White isn't taking anything for granted in regard to making the regular-season roster despite being owed guaranteed money by the team.
"Every year, you want to get what you deserve," the 26-year-old White said, per the newspaper. "All the hard work that I've put in, I want to pay off and things like that. But you can't control any of that. Just roll with the punches and try to work hard every day. Hopefully everything will work out."