As far as listening "real" time, you couldn't, but you could plug in the Flight number into any number of flight tracking sites to see which reporting facility of the aircraft they are currently pinging.
Flightaware, AirNav, Flightradar24, etc. Now it doesn't give you the EXACT center, or TRACON center they may be communicating with, but for example with Flightaware (pic attached), it helps narrow it down. I've used that many times when putting together audio clips (most I know off the top of my head) to see where they may be handed off too.
atleast seeing the reporting site, you can then pop that into LiveATC to see if there is any coverage in and around that site, or the Center frequency attached to it if there is coverage there.
Happy hunting !
John