Last week the striker’s legal representative Ricardo Cardoso threatened Chelsea with a lawsuit regarding the club’s treatment of the Spain striker, particularly their refusal to sanction his protracted return to Atletico Madrid.
And newspaper reports suggest that proceedings have now started.
Costa, who is not training at the club’s Cobham HQ, has accused Conte of informing he was no longer wanted via a text message during the summer.
Conte and Chelsea are adamant Costa was aware of the situation in January.
The Blues boss has insisted that it was decided in the New Year by Costa and his agent, Jorge Mendes, that the striker would leave the club in the summer.
On Friday, Conte on Friday said there was ‘no news’ on Costa and responded
‘I don’t know’ when asked when the striker might return to London.
A Chelsea spokesman added:
‘Nothing to report on that.’