The B737 aircraft was being radar vectored for an approach to Sydney runway 34. The Approach South controller issued instructions for the crew to expect runway 34 Right and proceeded to transfer the aircraft to the Director for final approach. The Director vectored the B737 onto base leg and then onto final approach with an instruction to intercept final for runway 34 Left. This runway expectancy was immediately questioned by the aircraft captain as he had briefed his crew for an approach to runway 34 Right. The Director confirmed that the runway would be 34 Left and commented that he thought the crew had already been given that information. The captain replied that he had not, but that the change to 34 Left could be safely carried out. The aircraft continued its approach and landed on runway 34 Left without further incident. It was determined that the coordination for the change of runways was carried out between the controllers concerned, but the exact manner in which this was performed was not established. The controllers did discuss the possibility of changing aircraft between the two runways in general terms, but there was no specific reference to this aircraft on the voice recordings. The flight progress strips, which may have provided further insight into this aspect of the occurrence, were not located during the investigation and were unable to be scrutinised. No definite reason for the failure to advise the crew of the change of runway could be determined.