The first-round draft pick will start the season on the physically unable to perform list, meaning he will be sidelined for at least the first six games. After six games, the Bears have until after their 11th game to activate him or shut him down for the year. Pace said it's possible that White could miss the entire season.
"He'll convert from active PUP to reserve PUP and then that gives us the option to bring him up in the latter part of the season," Pace said. "Guys, honestly, is there a chance that he misses the season? That's a possibility. I want to make sure we do this the right way, not rush him back. Sometimes I feel like you have to protect them from themselves."
White said he hopes he can play at some point this year but also said he'll listen to his body.
"If I can come back and am able to play a little bit in the season, we'll do it, if I'm feeling OK," he said. "But just following through. If they want me out there, then I'll try my best to get out there. I want to come back as soon as possible. ... If it's this season, then great. If it's next season then I'll just have to wait."
The Bears have not set a date yet for White's surgery.
"He's emotional," Pace said of White. "I know he sincerely cares about this organization, about his teammates, about coach [John] Fox. It's from the bottom of his heart, and that's why, to me -- and I know, this is kind of a weird time to say this -- but man, I'm telling you, that guy, it's confirmed to me the type of person he is, through this process."
White had been limited to pool and elliptical work until Monday, when the team allowed him to lightly run on a side field during practice.
"There was a setback," Fox said Saturday. "He looked pretty hopeful the first day [Monday] running on grass but not so much the second day. He's going to be a heck of a football player. He's a great young man. It's unfortunate it happened in the OTAs. We thought the rest might get it better but unfortunately it didn't. We need to fix it long term and get him ready to play his NFL career."
White's shin has been bothering him since the final week of organized team activities.
"I just got pain in that spot again," White said. "I'm not ignorant about the situation. I knew it would probably lead up to surgery so I've just got to accept it and roll with the punches. I was shut down ever since OTAs so I was pain free until I did running and it got a little aggravated again."
Pace said the Bears want to protect their investment in White and take a conservative approach.
"We were being very cautious," Pace said. "This guy's a big commodity for us. To me, it was kind of black and white. If he's having no pain, let's go, let's build him up slowly. Any type of setback, let's do the right thing here. To me, hey, it's unfortunate, but there's clarity in this is the surgery that he needs to have. It'll be successful."
Pace said the coaching staff noticed White limping toward the end of the offseason program.
"It wasn't a specific play where I said, 'Aha -- there it is,'" Pace said. "It was more like, because obviously you guys were at rookie minicamp and beginning part of OTAs -- explosive, sudden, we're all fired up. Later part of OTAs we all noticed it on the same day: 'Hey, he's limping.' And as we looked into it further, there's a small stress fracture down there. When we found that, it's like sometimes these things heal on their own. A lot of times they do. So that was our hope and that was our plan and unfortunately this is where we're at now."
Quarterback Jay Cutler spoke recently about how impressed he was with White's skill and determination to get on the field.
In other injury news, Pace said that he expects wide receiver Alshon Jeffery to play in the Week 1 opener against the Green Bay Packers. Jeffery suffered a mild calf strain on Wednesday, which will sideline him for roughly one week, a league source told ESPN NFL Insider Adam Schefter.