My guess would be very little. TO's old, on a 1-year deal (which actually is probably a positive at this point), and has done nothing on the field so far. Anyone trading for him is banking on the likelihood of Edwards royally sucking.
On the plus side, TO has shown signs that he might keep his mouth shut all year, which would be a selling point to a prospective buyer. Given how bad the QB play has been the past 3 weeks, I think most people are probably surprised that TO hasn't blown up on Edwards yet, either on the sideline or to the press.