The Spain international helped fire the Blues to Premier League glory last season but he revealed on Thursday that his time at Stamford Bridge is coming to an end.
Costa insists he has received a text from boss Antonio Conte, claiming he is not part of his plans for next season.
He has been linked with a return to Atletico Madrid and a move to China but now Milan have entered the race for his signature.
Following their recent takeover, the Italian giants are on the lookout for new signings as they try to challenge for the Serie A title.
Ricardo Rodriguez, Andrea Belotti and Alvaro Morata are also on their wishlist but Costa now appears to have shot to the top of it following his revelations.