The Ivory Coast striker signed for Chelsea from the French club for £24million in 2004, and has claimed he would always like to return to the Stade Velodrome before the end of his career.
Marseille president Jean-Claude Dassier said: "We want him but, honestly, we don't have the means to pay him.
"He is 33 and in great physical shape. We would love him to come back to us and I would therefore be an idiot to say we are not interested. All the big clubs are interested in him.
"We want to strengthen our squad but we have to watch our budget."