So far my experience with negotiations have not been positive. I have never had a manager accept my bids. This maybe because they are abandoned teams or maybe because they only login from mobile.
How's about....crazy idea....wait for it....
Awarding the player to the manager who makes the offer for any bids that are not responded to! At least it'll force the manager, if he is active to make the effort to reject/turn down the bids. And if it so happens to be an abandoned team, then it's a win win. Talent wont go to waste.
Yeah, wouldn't that be nice....but I doubt it'll happen.