Costa has been wanting to go from the moment he signed for us.
Every summer he's had to be convinced to stay. Costa himself told Conte last summer that he wanted to return to Atletico Madrid, which annoyed Conte. When the Atletico move didn't happen (they signed Gramiero instead) Costa said he had to go to Conte and apologise to get back in the good books again.
Then the China thing happened mis season, which forced Conte to drop Costa seemingly because he wasn't focused enough.
No surprises that as soon as the season finishes, Conte let's Costa know he can leave.