Narrative:

We were on an IFR flight plan; on autopilot and assigned a heading to intercept the localizer [for runway] 16 and regional approach told us maintain 4;000 ft. [Which] kept us in the dfw class B airspace. There were numerous VFR aircraft in the area operating under the class B shelf. One of the aircraft below us was indicating 500 ft. Below us on our TCAS at our 2 o'clock position and a couple miles. While looking for the airport we got a RA to monitor vertical speed. The aircraft that was at 3;500 ft. MSL had started a climb and was 400 ft. Below us. We tried to pick up the aircraft visually as he continued to climb. He came within 200 ft. Below us by the time we made visual contact. The traffic was in a steep left hand turn from our right to left. At no time were we told about this aircraft or issued a traffic alert from ATC. We were prepared to execute a climb if we would have gotten a climb RA. The pilot of the GA aircraft did query ATC to tell her that there was [an aircraft] that just went over him and that his instruments said that we were only 200 ft. Above him. Though the pilot of the GA aircraft queried ATC about us; he continued his left hand turn to only disappear behind our 7 o'clock position. The controller called us to check our altitude to which we responded that we were level 4;000 ft. And then I requested an updated altimeter setting which was only 1/100 different from what we had set. After losing sight of the GA aircraft we observed him descend back down to 3;500 ft. MSL. Because we visually acquired the traffic and no further TCAS alerts were received; no other action was taken by the crew. Though the controller was busy; it is troubling that we were not notified of the traffic considering the track and minimal vertical separation. It is also surprising that the controller's equipment did not issue a collision alert when the GA aircraft started to climb.during our brief prior to departure; we discussed the possibility of traffic underneath the class B and that extra vigilance would be required. I don't believe that the flight crew could have done anything differently. We were alert for a possible traffic situation in the dfw area.

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Original NASA ASRS Text

Title: Falcon 900 Captain reported an NMAC during initial approach without warning from ATC.

Narrative: We were on an IFR flight plan; on autopilot and assigned a heading to intercept the localizer [for Runway] 16 and Regional Approach told us maintain 4;000 ft. [which] kept us in the DFW Class B airspace. There were numerous VFR aircraft in the area operating under the Class B shelf. One of the aircraft below us was indicating 500 ft. below us on our TCAS at our 2 o'clock position and a couple miles. While looking for the airport we got a RA to monitor vertical speed. The aircraft that was at 3;500 ft. MSL had started a climb and was 400 ft. below us. We tried to pick up the aircraft visually as he continued to climb. He came within 200 ft. below us by the time we made visual contact. The traffic was in a steep left hand turn from our right to left. At no time were we told about this aircraft or issued a traffic alert from ATC. We were prepared to execute a climb if we would have gotten a climb RA. The pilot of the GA aircraft did query ATC to tell her that there was [an aircraft] that just went over him and that his instruments said that we were only 200 ft. above him. Though the pilot of the GA aircraft queried ATC about us; he continued his left hand turn to only disappear behind our 7 o'clock position. The Controller called us to check our altitude to which we responded that we were level 4;000 ft. and then I requested an updated altimeter setting which was only 1/100 different from what we had set. After losing sight of the GA aircraft we observed him descend back down to 3;500 ft. MSL. Because we visually acquired the traffic and no further TCAS alerts were received; no other action was taken by the crew. Though the Controller was busy; it is troubling that we were not notified of the traffic considering the track and minimal vertical separation. It is also surprising that the Controller's equipment did not issue a collision alert when the GA aircraft started to climb.During our brief prior to departure; we discussed the possibility of traffic underneath the Class B and that extra vigilance would be required. I don't believe that the flight crew could have done anything differently. We were alert for a possible traffic situation in the DFW area.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.