The 28-year-old Spain international striker is no longer in the plans of Blues boss Antonio Conte following the arrival of Alvaro Morata from Real Madrid.
Costa, who moved to Stamford Bridge for £32million in summer 2014 and has scored 52 goals in 89 Premier League appearances, has been linked with a return to former club Atletico Madrid.
That move can't happen until January because of the Spanish side's ongoing transfer ban and that has left Costa's future up in the air.
A move to AC Milan on loan for six months until he can return to Spain has also been mooted, but nothing has been agreed to date.
In the meantime, Costa's agent, Ricardo Cardosa, has revealed that the player is about to make it known he wants to leave Chelsea.
"We are going to use all legal mechanisms to hold Chelsea accountable for this behaviour, making it possible for Diego Costa to leave," Cardoso said.