My own idea would be to continue the circuit as intended. If the other chap(pess) is already on final, (s)he is sure to have gone by the time I get to final. And at any rate I can and must check runway availability before putting down...
One big caveat, however, a situation I lived one day: someone reported base when I has halfway downwind. I had got the plane in sight, separation was ample, so I continued the circuit as published (it is rather strict at that place). When turning final however I had the fright of my life when another plane turned up from my right - he had been in the circuit, unobserved by me, and he did have extended his downwind. I am sure he must have been nordo - which is allowed at said field.