Police say people across the city have been duped into parting with cash for the sets which are packaged in boxes and presented as brand new.
The TVs have been sold from the back of vans at The Fort in Easterhouse and Parkhead Forge retail parks.
Poilce are appealing for witnesses.
A spokeswoman for Police Scotland said: "I would urge members of the public not to be taken in by these fraudsters. If anything seems too good to be true then it usually is." Anyone who has been a victim of this crime, or has seen people selling goods from the back of vans, is asked to contact Baird Street CID on 101.