Flight Instructor on training flight with student reported a NMAC during descent to land.

Narrative

I don't know exactly when this happened; but I believe it was sometime between XA:30 and XA:40 Eastern time. It may have been just a few minutes earlier.My student and I were coming back into ZZZ to land. We were told to expect XXR and were being brought to a left base for XXR (we were coming generally from the north). Runway XXL was also in use. We were being vectored by ATC and were maintaining 3;000 ft. MSL. The Approach Controller instructed us to 'fly heading 140; enter a left base for Runway XXR; descend and maintain 2;500 ft. for traffic'. I read this back while my student (the Pilot Flying (PF)) bugged the altitude and heading and initiated the descent. The controller then gave us the traffic advisory of a B737 at our 3 o'clock descending. I was looking for traffic but did not have visual on them. However; I did see them show up on our Multi-function Flight Display and this indicated they were below us. We were now level at 2;500 ft.. I finally got visual on the B737 off to our right as they were about to pass below us. They looked very close to us; but I never felt like we were in an unsafe position. I looked at the altimeter and it read 2;460 ft. or so. I took the controls to make sure we wouldn't descend any more and at that same time; we got a traffic advisory in our aircraft that indicated the traffic was 400 ft below us. We were on the assigned heading of 140. The rest of the flight continued as normal with no issues and we safely landed the aircraft.I really think the Approach Controller had us begin our descent just a little bit too early. Had we stayed at 3;000 ft.; we likely would not have gotten that TA. We probably would have needed to be vectored out a little bit further to ensure that we would have enough space to lose our altitude to land; but it could have prevented this situation. I think we should have had more of a buffer between the two aircraft. I also could have done a better job at making sure my student didn't drop that 40' down to 2460'; but I'm also not sure that that would have prevented us from getting the TA. If I had visual on the aircraft sooner; it's possible this would have been prevented but they were being covered by our wing so I couldn't quite see them until the last second.