Kay has put in some fantastic defensive displays for the Canaries during his time at the club, but an agreement has now been reached for the 29-year-old to play his football elsewhere.
Upon announcing the news, Barwell caretaker manager Guy Hadland said: "After to speaking to Liam Kay tonight, and the club now looking to kick on, we have come to a mutual agreement for Liam to move on and play his football elsewhere.
"Liam has given excellent service to Barwell over the last three seasons and myself and Barwell wish him all the best. Good luck Liam."