According to Ric, the rumors around the Association hint that Vinny's job is history.
I also know that Paul's control of the franchise, by virtue of the fact the Clippers will do anything to keep him, is nearly absolute. As for the current head coach, Vinny Del Negro, the consensus around the NBA is that this first-round ouster is almost certain to cost him his job. There are plenty of contributing factors that led to their demise that Del Negro couldn't control -- Billups' Achilles tendon issues, Blake Griffin's high ankle sprain, to name two -- but owner Donald Sterling simply invested too much in this team to be out of the postseason already. If Del Negro stays, it's because Paul wants him to stay and I haven't heard from anyone that Paul is willing to go to bat for Del Negro in that way. I only hope that over the next few months Paul doesn't feign that he will have nothing to do with who gets the job next or del Negro not being retained. The only way that could be true is if he tells the Clippers definitively that he is not coming back; otherwise, they are assuredly going to be highly interested in who Paul thinks should run the team.
Before we make comments like, "Well, it is DTS we are talking about here", let us keep in mind that DTS is also a businessman and Chris makes money for him. He will make sure CP3 is happy enough to stay, even if it means not retaining Vinny. Also, I do not remember who first reported it but DTS did not seem happy after the Clippers lost Game 5 at home.