The Spanish worldwide, linked with Atletico Madrid last summer, is set to return to his spiritual home despite Federation Internationale de Football Association imposing a one-window transfer ban on the Rojiblancos.
However, with his heart set on moving to former club Atletico Madrid next term, Costa would have to wait until January to make a move to his preferred club.
This effectively rules out Chelsea's preferred solution to the mess they are in with Costa.
Conte has clashed with his employers over his handling of striker Diego Costa, who was told that he was not wanted by the manager in a text message, and the club's slow start to potential transfer deals. Costa has not mentioned any other club besides Atletico.
Besides which, the two clubs are presently millions apart on their valuations.
The Spain striker and Atletico Madrid have reached agreement where Costa would move to Spain in January.
The midfielder, who has three years left on his Camp Nou contract, has also attracted interested from Italian Serie A side Inter Milan, reported Spanish daily Marca.
Equally, the prospect of keeping him at Chelsea for six months is risky.
With the clock ticking, the Premier League champions have to hatch a plan like the one which helped Fernando Torres back to Atletico.
Chelsea remain confident of completing deals for Everton striker Romelu Lukaku, AS Monaco's Tiemoue Bakayoko and Manchester City's Willy Caballero and they have convinced their manager that negotiations are being handled correctly, despite the slow progress.