1117 GMT May 19, 2019
Costa made it clear at the turn of the year that he was interested in a big-money move to Chinese Super League club Tianjin Quanjin, the Daily Mail reported.
Chelsea resisted the transfer but the manager's mind was made up and there is no way he is changing it.
“I don't like to talk about players who are not here,” said Conte, speaking for the first time since the infamous text message sent to Costa at the end of the season to inform him he would be allowed to leave.
“In January, the Costa situation was made very clear. For the club, for him and his agent and for me the situation is closed.”
The Spaniard wants to return to his former club Atletico Madrid and has been granted an extended summer break in order to complete the transfer.
Having missed out on Romelu Lukaku, who joined Manchester United for £90 million, Chelsea has signed Alvaro Morata as his replacement.
Morata, who underwent a medical in London on Thursday, will cost a club record fee which starts at £58 million and could rise to £70 million.
“For sure this transfer market is crazy,” said Conte.
”Not only for this season, but now if you want to buy a simple player – a normal player – you have to start to think about spending €40 to €50 million.
“It's incredible this situation but there is this situation and we must live with it.
“Lukaku cost a lot of money but the same with [Alex] Lacazette and Arsenal who spent €65 million. For a right-back you spend €60-€70 million. This is the situation now.
“We must be very good and not make a mistake when we buy a player. You have to spend a lot and it is very important to make the right choice.”
Morata is expected to complete his move before the weekend and join up with the Chelsea squad on the next leg of its tour in Singapore.
“This is a good signing for us,” said Conte.
“Morata is a young player but he has a lot of experience and played in the past with Real Madrid and Juventus in the league and the Champions League.
“He's a good striker, a player with the right prospects for Chelsea. He will be our first-choice. He can show his value with us. He is young and can improve a lot.”
Chelsea faces Arsenal in Beijing later today before games against Bayern Munich and Inter Milan in Singapore.