A320 pilot reported NMAC on final approach.

Narrative

Enroute from ZZZ to ZZZ1 while on final; ZZZ1 Tower mentioned that there was traffic on down wind to Runway XXL. They gave the traffic a caution that A320 was on final and caution for wake turbulence. Shortly after that we received a TA and had traffic on downwind. It was hazy and we lost the traffic until 400 ft when my peripheral vision off my left had a Cessna 172 had turned final and was under our left wing within 100 ft. We are now parallel to each other. My First Officer (FO) had lost contact when the aircraft was on down wind and I was watching that I was stable since it is a short Runway. So; I lost contact of the traffic anticipating that they would be behind us rather than turn in next to us. My first thought was to go around however; if I did; this may have caused a catastrophic upset of the 172. It was a short time of 30 to 45 seconds when the 172 descended below our glide path. I was in such disbelief that traffic would turn into us rather than follow behind which would favor due to the winds. My big concern is that our passengers could have [found] this and put it out on social media. In the near future; I will not have tower let traffic turn into our position rather enter from behind.