The news was first reported by the Chicago Tribune.
An original hire of Bears head coach Lovie Smith in 2004, Toub's special teams units annually rank near the top of the NFL.
"Dave has been here every day that I've been here, so I think it's pretty safe to say that I kind of like what he does and he likes it around here," Smith said Monday. "But in the same sense I know that Dave has goals too that he would like to get accomplished. And every coach on our staff, especially coaches who have been on the staff for eight years, you would like to see them take another step. I know one of the things Dave would like to do is someday be a head football coach and hopefully he has that opportunity some day."
Complicating matters for the Bears is the fact Toub's contract is set to expire. In the event Toub fails to land a NFL head coaching gig, there is a possibility he could fail to receive an acceptable contract offer from the Bears. If the two sides are unable to reach an agreement, it's likely Toub would have little difficulty finding another special teams job somewhere in the league after the Bears' exclusive 15-day negotiating window closes.
"If he got a job somewhere else in the NFL, I'd be happy for him," Bears punter Adam Podlesh said. "This isn't the first time it's happened, and it won't be the last, in the event that does happen. I see it all the time. When it comes down to it, this is a business, and you have a job. You're looking for your best situation. Whether it's going a better job, or paid more money, or different title, which we won't go into specifics on, but I'd be happy for whoever does that. My job is to punt the football, and whoever is going to be coaching me, I'm just going to do the best job that I can."
Jeff Dickerson covers the Bears for ESPNChicago.com and ESPN 1000.