An unofficial group of NASA employees and veterans are spending their off-hours considering how to send a human crew to an asteroid. They're eyeing possible near-Earth objects as landing points, not the asteroid belt between Mars and Jupiter. The "Asteroid Underground" crew is analyzing all the details, from the tech needs to the trajectories to the scientific potential of such a journey. From Air & Space Magazine:
The group also wrestled with the problem of communicating with a spacecraft more than two million miles from home. "At even a near-Earth asteroid, you're 10 voice-seconds away," says (NASA engineering Dave) Korsmeyer. "You're not really conversing with Earth at that point. The whole nature of the interaction becomes like the old ship-to-shore communications, a fancy telegraph, a voicemail. Not in real-time."
An asteroid-bound crew would therefore need to "bring mission control on board," says Korsmeyer, in the form of highly automated decision-making software. "When something bad happens, which tends to happen quickly, the crew and systems will have to manage it on their own. This is something humanity hasn't done yet. But that makes it the best of all possible testing grounds for Mars, which, without an asteroid mission, will be like jumping into the deep end without practicing in the shallow end." In comparison, "the moon is like the baby pool. I don't mean to minimize that–Apollo 13 showed us you can drown there too." But, he says, an asteroid "would really be someplace fabulously new. You're talking 2.5 million miles, more than 10 times the distance between Earth and the moon. You'd be so far away you could cover up Earth with your finger. It would be no more than a beautiful, pale blue star."