The Blues forward struck the equaliser as Arsenal triumphed in the FA Cup final and is seemingly out of favour with his Italian boss.
Costa was an unused substitute for the friendly vs Colombia and told the media afterwards that the former Juventus chief has texted him to inform him would not be in his plans for next season.
Costa hit 20 Premier League goals to inspire the Blues to a second title in three years, but speculation over a move to China in January appeared to affect his form.
The forward has been pushing for a return to Atletico Madrid for some time and was pictured with Diego Simeone earlier in the season – which appeared to anger Conte.
Los Colchoneros have a transfer ban until January 2018, which may complicate his departure from Stamford Bridge in a World Cup year.