Small Transport; Low Wing; 2 Turbojet Eng
Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP)
Flight Crew Last 90 Days 125; Flight Crew Total 9400; Flight Crew Type 1300
Communication Breakdown
ATC Issue All Types; Conflict NMAC; Deviation / Discrepancy - Procedural Clearance
Flight Crew Took Evasive Action
Airspace Structure; Human Factors; Procedure
While within the class B airspace; 10 miles North of ZZZ; we called the airport 'in sight' and were cleared for a visual approach to ZZZ runway XX. As we began our descent from 4;000 MSL; we noticed a target on TCAS 500 ft below our altitude approaching our path from the East. We stopped our descent while looking for the traffic. Then the [TCAS] commanded a climb as the aircraft neared our location. We began a climb as the aircraft passed below us. When TCAS stated clear of conflict; we continued our approach to ZZZ. I reported our conflict to ZZZ tower; and we were cleared to land on XX. VFR traffic below the Class B airspace combined with our clearance for a visual approach contributed to our conflict within 500 ft vertical. We never saw the other aircraft. [TRACON] was busy; but a warning that the aircraft was below us and converging on our track to the airport could have delayed our descent; and avoided the conflict.
Small Transport pilot reported a TCAS warning on initial approach.