It's a tough thing to cast someone like Sinatra. While I certainly like all three men as actors in their own right, I think their own fame makes it impossible for them to disappear under the skin of an icon. This isn't exactly Howard Hughes or John Dillinger, figures that an actor can shape from facts and bits of footage, but still make their own. This is a man we're all familiar with from countless movies, concerts, albums, and television appearances. How do you portray that honestly with Depp, DiCaprio, or Clooney? If forced to choose from the three, I'd pick DiCaprio purely because of the physical resemblance, and politely suggest Clooney play Dean Martin.
Personally, I hope Scorsese finds a semi-unknown for the part (someone on the level of Tom Hardy -- who might actually be really good now that he's sprung to my mind) and steers clear of the A-List. The actor lucky and brave enough won't have to sing, as Universal and Mandalay spent 2 years clearing the rights to Sinatra's catalog, but he still has to be someone you believe to possess that voice. Would you cast one of the Big Three above? Or do you have someone else in mind?