The post on the club's official Twitter feed read: "Angleterre Ashley Cole arrière gauche sera un joueur Rouge et Bleu cet ête".
Translated into English, this says: "England left-back Ashley Cole will become a Red and Blue player this summer."
Cole's current Blues contract expires at the end of the season, meaning his future his been the subject of much debate so far this season.
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New Chelsea boss Rafael Benitez said on Friday that he did not expect Cole, and Frank Lampard, to remain at the club in the long term and when asked if the pair were likely to leave soon he said: "I think so.
"I don't have all the information and it's not fair to tell me I'm only here for seven months and then expect me to have an influence at the club over the next two or three years, but I think that's the case at the moment."