MD88 EXPERIENCED NMAC WITH TFC WATCH ACFT DURING VISUAL APCH AT BHM.

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WE WERE INBOUND TO BHM ON RADAR VECTORS AND DOWNWIND. WX WAS VFR. WE WERE TURNED BASE AT 4 MI AND ASKED IF WE HAD THE FIELD. WE REPLIED THE FIELD WAS IN SIGHT; AT WHICH TIME THE CTLR CLRED US FOR THE VISUAL APCH; TOLD US TO SWITCH TO TWR AND ADVISED 'THERE IS A TFC WATCH CESSNA SHORT FINAL.' I THOUGHT IT MUST BE LNDG AND WAS CONCERNED WE WOULD BE CLOSE UNLESS WE EXITED THE RWY EARLY GIVEN OUR SPD OF 220 KIAS. I DID NOT SEE HIM WHERE I THOUGHT HE SHOULD BE. A TARGET WAS ON TCASII DIRECTLY ON OUR NOSE AT 2100 FT MSL. WE WERE AT 2400 FT AND DSNDING. I LOOKED UP TO SEE THE CESSNA FLYING AWAY FROM THE RWY ON A COLLISION COURSE WITH US. I CALLED FOR THE COPLT (WHO WAS FLYING) TO CLB AND THE TCASII GAVE AN RA 'CLB; CLB!' THE CESSNA PASSED BELOW US FROM R TO L HAVING NEVER ALTERED COURSE. WE SHOULD HAVE BEEN TOLD BY APCH THAT THE TFC WAS PRESENT PRIOR TO CLRING US FOR THE VISUAL APCH. THE FACT THE TFC WAS MOVING AWAY FROM THE ARPT AND ON A COLLISION COURSE WITH US SHOULD HAVE KEPT THE CTLR FROM ISSUING AN APCH CLRNC AT ALL. HAD I KNOWN THERE WAS TFC THAT CLOSE (MUCH LESS HEADED MY DIRECTION) I WOULD NEVER HAVE TURNED BASE. A VISUAL APCH WOULD HAVE BEEN OUT OF THE QUESTION. IF NOT FOR VISUALLY ACQUIRING TFC WE DID NOT KNOW WAS THERE AND THE TCASII RA; A COLLISION WAS ALMOST SURE TO HAVE OCCURRED.