Evina, who is out of contract, turned down the club's initial offer of a one-year extension at the end of last season.
Charlton made a new offer to the Frenchman, but after failing to agree terms with Evina they have decided to take the deal off the table.
Evina has not travelled with Charlton for their training camp in Spain and he is training on his own as he looks to fix himself with a new club.
The former Arsenal youngster's representative, Saif Rubie, admits the player has been left in 'no man's land' after Charlton withdrew their contract offer.
"Charlton did not want to compromise on a new deal and now my player is left in no man's land," Rubie told Sky Sports.
"We are now looking for another club for Cedric and he is training on his own to maintain his fitness so that he is ready to go straight into a new club."