Air carrier Captain reported an airborne conflict with a UAS while they were on initial approach and notified ATC.

Narrative

I was Pilot Flying. At approximately XA:45z; at approximately CADUS intersection; established on the ILS 36L approach into MEM at approximately 2000 ft. MSL; out of the corner of my eye I saw what appeared to be a black object (what I thought initially was a bird) at our 10:30-11:00 position. I remember thinking that it was strange to see a bird at this altitude in this weather (an undercast layer was just below us; and a higher overcast layer above us). It was then that I turned my attention to the 'bird' and realized that it wasn't acting like a bird. It stayed at the same altitude; and didn't appear to be 'flapping' any wings. In addition; it did not veer off or change directions like a bird would (e.g. climb or swoop down and away from us). As the object/bird came closer to us it 'zoomed' past us up and to our left. I turned to the First Officer and said; 'What was that?!'. It was at about this same time that we started our descent from 2;000 ft. into the undercast layer after capturing the glide slope. The total time that I had eyes on the bird/object was maybe 2-5 seconds. It is my belief that the object was actually a drone. It was much bigger than the average sparrow/swallow; but not as big as a bird of prey. Everything happened so quickly that I cannot provide much more details. We were aware that there were aircraft on the approach behind us; so in an effort to enhance awareness and safety we reported what we saw (and believed to be a drone) to Memphis tower. At no time did I feel that the drone/object struck the aircraft. However; it's relative position to us was such that had we been a little faster we could easily have collided with this object.Cause: Possible drone on approach/flight path into Memphis.