Peppers is the top free agent in a market that opened at 12:01 a.m. ET Friday.
The 6-foot-7, 283-pound Peppers is a five-time Pro Bowler who recorded 10.5 sacks with two interceptions and five forced fumbles last season.
"If we bring in Julius Peppers, that could help us a lot," Bears defensive end Alex Brown said Thursday on "The Waddle & Silvy Show" on ESPN 1000. "The guy's a monster, he's an animal. He's the biggest guy and fastest guy I think I've ever seen."
Peppers' impact could be so important to the Bears that Brown would be willing to move from right defensive end to the left side.
"He's as gifted as [linebacker Brian] Urlacher, I think," Brown said Thursday. "He's just about 30 pounds heavier. He's unbelievable.
"He could definitely help our team."
Jeff Dickerson covers the Bears for ESPNChicago.com.