The French club agreed to a full time switch after West Ham expressed an interest in the player.
"Marseille is definitely the choice for Djibril. I think the deal will happen on Friday or Saturday," said Cisse's agent Ranko Stojic.
"I have been very busy this week - I caught six planes in two days - and I am sorry for the people I have not had the chance to call back, Mr Eggert Magnusson of West Ham for example.
The Marseille option is the best choice for Djibril because of the Champions League.
"West Ham, Bolton and Portsmouth I understand are very, very good clubs but Djibril wants to play in the top level of European competition next season."