Well he has the right to say no.... But if the club want him out, then he really has only one option... The club can cancel his contract (like they did with Vieri and Figo)
In theory, yes, a player can refuse to sign a new deal with the buying club, and the transfer collapses. Of course, he now knows that he's not wanted by his current club. A contract cannot be cancelled unilaterally without cause. The player would be entitled to a buyout (unless the contract specified otherwise). Contracts can be cancelled by mutual consent (I think that was the case with Vieri). For example, Luis Figo's contract has not been cancelled, in fact Real Madrid want a transfer fee from Liverpool.
It all depends on what is the player-manager contract like. Here, we had a lot of cases where young players, enthusiastic because of the start of their career would sign anything, without reading the contract or some legal advice. In the end, the manager would simply own him. When it comes to clubs, I guess no club will buy a player who openly says he wouldn't go there.
more importantly, they wouldn't be able to. It isn't possible to transfer a player against his will. Players' contracts can't really be cancelled either. In some cases clubs will pay-off an agreed proportion of a player's contract to get him off the wage bill, but it's still up to the player if he agrees to it or not.