Evina, whose contract at The Valley expired on July 1, featured in Saturday's opening pre-season friendly against non-League Welling but failed to report to the airport on Sunday for the club's week-long training camp in Spain.
Contract talks between the two parties have currently broken down but, despite reports suggesting Charlton's offer no longer stands, manager Chris Powell still wants to strike an agreement.
Powell told the Addicks' official website: "It's an issue that has been ongoing for a long time and should have been something that was resolved as soon as the season ended.
"We got very close last week and right at the last minute they changed it again. Ceddy is well within his rights to turn it down and his Dubai-based agent has advised him not to sign."
He added: "There has been a lot of toing and froing but Ceddy has come back this summer and trained really well. His testing has been good and he played at Welling.
"I've told him how much I want him to stay. He's had two years here and he's a young man who has got the ingredients to be a good left-back. He's starting to show that. He hasn't really had a career yet and I want him to have that here.
"I work with him every day, along with my coaching staff and my players, and he's a character that fits in really well with us."