Flight Crew Air Transport Pilot (ATP)
Situational Awareness
Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Issued Advisory / Alert
Human Factors
Abeam the field for a left downwind to runway 34L at 8;000 feet; approach queried if we had the field in sight. We reported we did and were cleared for the visual approach to runway 34L. (Sequence was number 1).  We were west of the 34L LOC course at 8;000 between DUNLP (8;000) and FLLAG (6;100).  We made a left turn to intercept the ILS 34L on a 45 degree intercept and commenced a descent to 6;100 feet to arrive just outside of FLLAG on the ILS. We were VMC and clear of all terrain. Passing 6;600 feet and .5 miles from intercept of LOC; SLC approach gave us a 'Low Altitude Alert; below Minimum Safe Vectoring Altitude'. We leveled off and replied we were on the visual; clear of terrain; and intercepting the LOC. Intercepted ILS 34L just outside of FLLAG at 6;200 feet. Landed uneventfully. Submitting report for information. Do not feel any violation or safety concern occurred. We do appreciate the controller looking out for us. Heads up on his part; however in this case it was DAY VMC and we were well within parameters for visual approach maneuvering. Again; though; we appreciate the information from ATC. [Suggest] a refusal visual approaches? Not always feasible; but will certainly play a larger role in my decision matrix from now on.
Air carrier First Officer reported ATC issued a low altitude alert to them on a visual approach to SLC.