The 25-year-old has started all regular season games over the last two years for the NFC North side, but allowed Carolina Panthers defensive end Charles Johnson through to sack Jay Cutler during their pre-season game on Friday.
The head coach told the Bears' official website: "He's in a competition, we've told him that he is. I said earlier in the week I didn't hide from the fact that he's had very good days and not so good days.
"He hasn't been as consistent as we'd like, and we'll look at the tape and see where he is, but when he's on his game, he can be very good.
"I know [assistant coaches] Aaron [Kromer] and Pat [Meyer] are working hard to create an environment for him that he's more successful."
Webb was drafted by the Bears in 2010.