Even the closest near-earth asteroids would be considerably more difficult to get to than the Moon, which is after all reasonably close and a reasonably big target.
The problem with the Moon is that it's somewhat light on the periodic table. A lot of Titanium and silicates. And no tectonic activity to keep churning up the heavier stuff to the surface as on Earth. The great thing of course is what everyone knows, the moon is prime real estate. As they say, "Location, location, location."
Rendezvous with an asteroid is no problem, NASA/JPL already has a great deal of experience with that. I have no idea if anyone's realistically tackled the technical challenge of how to dig, or refine/smelt ore in zero-g. Then, moving either the ore or the asteroid to a commercially lucrative orbit can easily wipe out any profit, or take years of waiting.
It may be possible to send an automated probe that constructs mining and refining facilites out of the asteroid material itself, and/or builds solar panels and an electromagnetic mass-driver to either launch ore pellets back to Earth or wherever it's desired, or act as a rocket to move the remainder of the asteroid itself.
However, now we're talking both pie-in-the-sky technology, and huge sums of money and a long period of time to realize a return on the investment. Also, such an asteroid so outfitted would not only be a mine, but a rather potent
weapon. Either the launched ore pellets, or the whole asteroid itself. :|
Although, such high levels of automation, engineering, and materials handling may be post-Singularity technology, so the current crop of economic and military paradigms may not even be applicable anymore.