I'm guessing via gravity, but I think drawing something big enough to attract space junk close enough to attract space junk will be too dangerous for earth.
That's not really how gravity works. In low earth orbit you have thousands of objects moving at high relative velocities, which is why they are dangerous. You can't just "attract" them with the gravity of a large object, all you would do is deflect them a little. They are moving fast enough that the gravity of a large nearby planet (Earth) is only bending their path enough so that they don't escape completely. An asteroid in LEO would do pretty much nothing to change that. You just might be able to deflect some (very small) fraction of the objects into different orbits, maybe enough so that they reenter the atmosphere. But most of them wouldn't interact at all.
I was actually thinking deflection. Assuming they're going to bring it near Earth anyway, why not, say, slowly circle the ISS? Sure, it wouldn't do MUCH good... But it's the biggest space squeegee we're going to have access to for the near future...
Could a large body like an asteroid be used to clean up space junk? Or would that just be way too risky?