This article points out some interesting possibilities, but I don't think most of them will work.

The Bears couldn't simply offer a draft pick and an unproven player. It would need to be a pro bowl level player.

They're not going to want to damage their nucleaus of defensive talent, which is Harris, Briggs, Alex Brown, Urlacher, Tillman.

Even though Urlacher "ain't what he used to be" He's still very good, and the MLB is important in the Bears system.

In total, I just don't think the Bears have the resources to oust another team in a trade for Him.