I think we're better off prepping a mission to the next interstellar visitor than trying to catch up with the last one. In a few years, our detection technology will be a lot better, we'll have time to get ready and the sooner we launch the better for this type of mission. A high relative velocity one-way fly-by or even a deliberate collision might be possible even with current chemical rocket technology, given enough time to get ready. But I doubt matching speeds with it would be realistic without some sort of exotic propulsion system.

One of the big problems with Clarke's Rendezvous with Rama was that the Earth spacecraft sent to intercept it was able to come alongside the object at all. One would expect that any extraterrestrial craft would pass through the solar system at velocities which would demand relativistic speeds on the part of the pursuit craft, even if the pursued object was NOT traveling at relativistic speeds.. And of course, you have to brake to be able to come alongside and board it!