Essien has started just two League games for the Blues this season.
Piveteau told French radio station: “[Essien] could leave Chelsea this winter.
“Several major European clubs playing in the Champions League were informed and the situation should settle down within the next 10 days.
“You should know that Michael was not on the list of players who can play in the Champions League with Chelsea, so he is free to play in the competition with another club.”
His agent also refuted reports that Essien may return to Bastia.
“A come-back at Bastia? We must stop with this,” he said. “Michael plays at Chelsea, a big club. In Ligue 1 he could play only at Paris Saint-Germain, Lyon … But Bastia, FC Sochaux – without disrespect, no. For them to support the salary of a Chelsea player, it is already impossible.”