The 21-year-old Cameroonian rejected a one-year extension last season before the Addicks returned with fresh terms.
However, the Championship side have now pulled out of a possible new deal, leaving the full-back as a free agent.
"Charlton did not want to compromise on a new deal and now my player is left in no man's land," Saif Rubie told Sky Sports News.
"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."
Evina, who started his career with Arsenal, joined Charlton from Oldham Athletic in the summer of 2011.