We define a Nash bargaining solution (NBS) for partition function games (PFGs). Based on a PFG, we define an extensive game (EG), which is a propose-respond sequential game where the first rejecter of a proposal exits from the game with a positive probability. We show that the NBS is supported as the expected payoff profile of any stationary subgame perfect equilibrium (SSPE) of the EG such that in any subgame, the coalition of all active players immediately forms. We provide a necessary and sufficient condition for such an SSPE to exist. We also present an example in which delay of agreements occurs.