No, I think Ray Allen stays put. I do not deny, however, that Danny Ainge is calling other GM's (and receiving offers for Ray) in order to evaluate Allen's perceived worth around the league. This may be used as a benchmark to assess Ray's comparative value to players desired around the league. But Ainge seems to do this with every player on his roster, as a way of keeping up to date with the trade market.
I think, honestly, that with the release of Lester Hudson, Ainge is more interested in finding a player through waiver wire or buy out to fill the final and 15th roster spot. This might lead to a minor trade involving Big Baby perhaps (or the other way around). Rest assured, if Ainge is watching this team as closely as we all are, he knows they won't win a title standing pat. But I doubt he will go as far as to trade Ray Allen. But I could be wrong.