Possible, maybe. Little or cheap, definitely not. Both Voyager probes relied on a unique alignment of the planets in the outer solar system that allowed them to get a series of speed boosts using gravity assists from the gas giants. If we wanted to launch a rocket anytime in the near future that would be able to catch up with Voyager 2 we'd probably have to rely on good old fashioned brute force (rocket power). But then if you want the rocket to catch up in the next thousand years it's going to need REALLY big ass rockets to catch up with Voyager... and if you want it to rendezvous with Voyager instead of just zipping past, it will need to haul more rockets all the way out to Voyager so it can slow down and match speeds (which means even bigger rockets to launch from earth, etc.).
tl;dr - space is big and the rocket equation is brutal.