Air carrier Captain reported seeing what appeared to be landing lights descending toward their aircraft during approach and took evasive action to avoid a collision. Reportedly; air traffic control had no observed traffic on radar at the time.

Narrative

While being vectored for an ( ILS22 / visual) approach to 22L; I took over control from the First Officer (FO) to avoid another aircraft (A/C) or drone. While at approximately 3;100 ft. on a left base into Boston; I looked out the left window to see what appeared to be landing lights descending in on our A/C. I climbed our A/C and distinctly saw the light pass underneath and slightly behind our position. Once clear of that traffic; I transferred control back to the FO; and since we were still able to have a stabilized visual approach; we continued for a normal landing and arrival into Boston. I was told by ATC at the time that there were no observed traffic relative to our flight path. Later I checked with an approach controller that had no observed traffic on radar at the time. However; while walking out of the terminal; I was stopped by two customers; that were in row 2 on the left side of the A/C. They thanked me for keeping them safe; as they personally viewed the lights as well. Their story was the same: a descending A/C into our flight path sliding behind and underneath as we climbed.I can only speculate that this was a plane with no transponder on a full moon night; or drone; as it was a crystal clear evening; and both myself and multiple customers witnessed the same thing.