The Stamford Bridge club are set to complete a £60million deal for Everton striker Romelu Lukaku in the next few days – but it could be the signal for Costa to return to his former club Atletico Madrid.
Atletico have been chasing Costa, 27, all summer and are ready to pay £40m for the Spanish international striker.
Costa, who cost Chelsea £32m when they signed him from Atletico in the summer of 2013, has made no secret of his wish to return to Spain.
He was again absent as Chelsea lost 3-2 to Real Madrid in their second International Champions Cup game in Ann Arbor, suffering from a back strain.
Just after Italian Conte was appointed, Costa had told him he would stay – but Atletico have never given up the chase, and after the game Conte said: “I can say that today Costa is a Chelsea player.
“Tomorrow if you ask me if Costa will remain with us, I don’t know.
“He didn’t play in these games because of injury and if he solves the injury and I see in training he’s in good shape it can be possible to see him in the next game against Milan. But I can tell you only that.”
Atletico though on Saturday signed French striker Kevin Gameiro from Sevilla in a £28m deal – so if they are to finally bring Costa back home they will have to sell.
On Lukaku, Conte said: “I don’t want to speak about players of other teams. This is not respect for the club or for my players.
“The transfer market is not the most important thing. The important thing is to build and be a team, always, in good and bad situations.
“It’s important to concentrate and work together without the ball. I know it’s tiring without the ball but important to stay together and stay compact like we did against Liverpool.
“If we think one two three players don’t want to work without the ball it’s possible we will see another bad season.”
Chelsea were 3-0 down after a horror show of a first half in Michigan, as Marcelo scored twice and Mariano Diaz added a third.
Conte made numerous changes at half time and Chelsea improved as sub Eden Hazard scored twice late in the match. They now face AC Milan in Minneapolis on Wednesday.