The Romanian forward is seeking a new club after Cesena were relegated from Serie A last term.
"We have an agreement with Mutu and with his agents,” said Ajaccio president Alain Orsoni.
"Now the player needs to agree terms with Cesena. Mutu, 33, is an excellent attacker and I hope he can wear our colours as soon as possible."
Mutu signed a two-year deal with Cesena last summer after being released by Fiorentina, but must hope his old club agree to a similar agreement as he bids to relaunch his career in France.