100% players have a right of veto for trades.He would have gone to the draft. Which is exactly what Reid would threaten to do if you didn't trade him where he wanted to go. If he wants to leave West Coast have no control of the destination under the current system.
Say West Coast wanted to trade Reid to the highest bidder, he can say no. In American sports they don't have that right.
For the Eagles, need to either sign him up for more years or trade him now and get the best deal they can that Reid will agree to. Reid out of contract and requesting a trade is a very bad outcome for the Eagles.