Boeing Company Undifferentiated or Other Model
Flight Crew Multiengine; Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument
Communication Breakdown
ATC Issue All Types; Conflict NMAC
Flight Crew Took Evasive Action
Human Factors; Procedure
Direct to LIT on the HOBRKK3 arrival at FL390. ZME Controller started a step down descent from 390 to 370; then 350; then 330. Same controller handed us off to another sector while descending to FL330. I was the PM (Pilot Monitoring) and checked in with the new sector. After 3 attempts the controller responded and asked if we were descending to 330 as if he was not sure why we were descending to 330. He immediately turned us to a SE vector due to traffic. TCAS generated a TCAS ALERT on a target under us. The TCAS alert generated a miss distance of <400 feet. I queried the center controller and informed him that I was concerned about the previous controller descending us into another flight directly below us. He was hesitant to respond; and in my opinion possibly didn't know we were descending to the FL330 altitude. Why; I don't know. I called ZME and had a conversation with a Supervisor and he told me a higher level manager would review the event and call me back later in the day but I never received a call back. I discussed this event with Captain (Name) and we both agreed that a conversation would be appropriate and to follow up with this  report. Obviously I do not have access to radar or audio recordings of the event and this narrative is the best info I can provide based on our experience. My crew followed each command from Memphis Center. I do not have internal ZME communication/coordination practices.
Air Carrier Flight Crew reported TCAS Alert on descent.