No, and there is no real way to short it, unless you can convince someone to create a derivative based on some of the loans and bonds that convert to Uber shares on maturity. The article discusses several ways you might be able to short Uber, but concludes that none of them are really available. It’s quite a good read.
It might be fun to short it at an IPO if and when they do one, though. Right now, by essentially not allowing shares to be sold, they can keep a lot of information to themselves, and the illusion of immense worth afloat.