Chelsea today announced Italy manager Conte will replace interim boss Guus Hiddink at the club after Euro 2016 .
And his first job will be to convince Costa to stay.
The Spaniard is looking for a way out of Stamford Bridge. The striker is currently serving a three-match suspension after being sent off against Everton for a clash with Gareth Barry.
And Costa is said to be frustrated at the prospect of a season without Champions League football even though Conte has vowed to return to the top four in the Premier League.
Atletico Madrid are interested in offering the prolific forward a return to the club where he won the league title in 2013/14.
And Costa's agent Jorge Mendes has also sounded out Paris Saint-Germain while the Chinese Super League has been mooted as a potential destination.
But the Brazilian-born goal-machine still has three years left on his contract at Stamford Bridge meaning it will likely take a very large bid indeed to part Chelsea with their man.
And his priority is said to be a return to Spain as he is fed up with what he sees as draconian punishments imposed on him by the English footballing authorities.