Spanish publication Marca reported on Tuesday that the Brazilian-born international, who joined Chelsea for 32 million pounds last year, had spoken to Atletico Madrid about returning to the club.
"He's the guy responsible for everything good we have in the dressing room. He's so happy, he's so funny, he's enjoying every minute," Mourinho said after the English champions beat Sydney FC 1-0 in the final match of their season.
"He's the happiest guy in the dressing room so if this is unhappiness, I'm happy with that.
"I think he was not happy with the news and I think in his bad English he has to try and address that he’s not happy with the news."
Costa was named Man of the Match despite being substituted before the end of the first half of the friendly that attracted more than 83,000 fans to Sydney's Olympic stadium.
"Diego was trying, we didn’t want to risk him (but) I told him 'let's give the fans at least half an hour of Diego Costa'," Mourinho added.
"He went until the 40th minute and at that time we all felt that was enough."
Mourinho paid tribute to all his senior players for the effort they put in out of "respect" for the fans, despite the long season they had endured.
The Portuguese was less impressed with the younger players who came on later in the match and almost let the hosts back into the game.
Mourinho was scathing of home-grown midfielder Reuben Loftus-Cheek who replaced Costa but was substituted himself half an hour later.
"He has to learn that at 19 you have to run three times as much as the other guys and you have to play in your limits and you don't have to play like a superstar with the ball at your feet because this is not the under-18s," Mourinho said.
"I don't accept that a player ... when we don't have the ball, doesn't press, he doesn't have intensity and he is waiting for other people to recover the ball.
"I don't accept that in superstars and I don't accept that in a 19-year-old kid. He has to learn what it takes to play for us."
(Editing by Tony Jimenez)
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