The player found himself in hot water with the fans and the club after his antics during the 20th Hillsborough Anniversary Service at Anfield in April this year.
He was told within weeks of the incident that his future lay outside of Anfield.
Some media outlets are reporting the deal with Kavala to be a permanent one, but the French media are reporting that the player will go on a season long loan with an option to purchase the player at a reduced valuation if the loan spell is a success.
Several deals for the player have fallen through over the course of the summer for the player.
Itandje played 7 times for Liverpool since his arrival in 2007.