Airbus pilot reported they were issued a takeoff clearance from ATC; and then issued a rejected takeoff clearance in the low speed regime. Another aircraft was on final and passed overhead the same runway as the Airbus as the Airbus rejected the takeoff.

Narrative

We were cleared to line up and wait Runway XX. We heard an aircraft say they were on base. We did not hear a runway (rwy) associated with the call. We were cleared for takeoff and began our takeoff roll. Then we heard high and continuing. We did not hear the rwy associated with the call. Tower immediately told us to reject. I had not called 80kts but the max brakes applied themselves so we were above 72 kts when we rejected. We never saw the other aircraft but we did see his shadow as he passed over us. Taxi off the active and then back to the gate were both uneventful. We refueled; refiled and departed two hrs later. Cause-Personally; I believe the tower controllers lost situational awareness of the aircraft in and around their own airspace. As a result; they cleared us to takeoff when another plane was on final.Suggestions-NOT CAUSAL - Standard procedures. Several times; Tower cleared airplanes to line up and wait after the Citation or GulfStream that is on one final lands. Maybe that's legal; but I've never heard it before and it leaves room for confusion for one; such as myself; that doesn't know the type of every plane flying. I don't know the legality; but I believe they should wait until the landing traffic has actually landed before direct the waiting traffic to line up and wait. CAUSAL - Comms. Tower ignored or didn't hear repeated calls from the plane calling base and then high on glide slope. That plane finally caused Tower to direct us to reject our takeoff. At all levels; missing calls occasionally happens but occurrences are decreased if procedures and comms are standardized and when there are two or more people listening. If they don't have one; maybe ZZZ Tower should have a supervisor who is on freq.