Air carrier Captain reported tracking a target on TCAS during final approach without making visual contact. After landing a passenger mentioned seeing a UAS pass the aircraft.

Narrative

Descending into DSM; cleared visual approach to RWY 31. Approach then called out VFR traffic about left 11 o'clock low; (can't remember the range; but I think around 5 miles) not talking to approach so they suggested we 'square off' our approach to avoid; which we did. We picked up the traffic on TCAS; about 1000' below at 10-11. Approach continued to advise us of the traffic at around 2100-2200'. We made the assumption it was a light aircraft or similar and actively searched for it but never saw it. We continued our descent and intercepted final. The TCAS target moved back to 11 o'clock and the altitude difference kept shrinking as we turned and we disengaged the autopilot and stopped our descent on the approach; leveling off around 2400 or 2500'. It almost seemed like it was trying to intercept us. After the TCAS display showed it moving behind; we resumed descent on the visual approach; which required a steeper than normal descent. After parking; while the passengers were disembarking; one told the FO they had seen 'a red drone' off the left side. If the passengers saw this; I think that would qualify as a Near Midair Collision. Amazing a drone would be operating at the FAF at or near FAF altitude.Cause: Some kind of aircraft operated in an approach corridor which caused a close encounter with our IFR arriving aircraftATC; equipment and pilots all functioned as they should have to prevent a collision.