While there's been speculation that the Warriors would only attempt to unload big expiring contracts like Andrew Bogut, Richard Jefferson, and Andris Biedrins if Dwight Howard chooses Golden State, that's not necessarily the case, according to Ken Berger of CBSSports.com. Berger reports that even if Howard commits to sign elsewhere, the Warriors are still interested in trying to clear cap space, perhaps to pursue another impact free agent such as Andre Iguodala.
According to Berger, the Warriors have offered Bogut, Jefferson, and Biedrins to the Hawks, Jazz, and Cavaliers, three of the only NBA teams with enough cap room to absorb one or more of those contracts without sending out salary in return.
Berger writes that Golden State would have to move two of those three players in order to clear enough space to sign Howard outright, though I believe all three would actually have to be dealt. Even if the Warriors were to move the two larger salaries (Bogut and Jefferson), the team would still have about $45MM left on its books, by my estimation. That would rule out a max offer for Howard, but would likely be enough room to squeeze in a competitive offer for a player like Iguodala.
While Bogut has a little value on his own, Jefferson and Biedrins, who are making $11MM+ and $9MM respectively, have significant negative trade value. I'd imagine that any team taking on either of those players would demand multiple draft picks, including at least one first-rounder.