Costa has been an instant hit at Stamford Bridge since arriving in a big-money move from Atletico Madrid, taking his tally to seven goals in his first four Premier League by scoring a hat-trick in Saturday's 4-2 win over Swansea City.
The Spain international's form is even more impressive considering he has been struggling with a hamstring issue that threatened to keep him out of Chelsea's top-flight fixtures with Everton and Swansea.
The same issue affected Costa during the recent international break, when the striker managed to participate in the 1-0 friendly defeat to France, but was unable to feature in Spain's 5-1 defeat of Macedonia in their Euro 2016 qualifying opener.
Chelsea boss Mourinho revealed that he considered resting Costa against Swansea in order to safeguard his fitness, but the 25-year-old was keen to play.
"The most important thing of a player's character is what affects his performance as a player," Mourinho is quoted as saying by the British press.
"Diego was a risk and a doubt before Everton, a risk and a doubt before Spain, a risk and a doubt before this Swansea game and he played all three games.
"He is a risk and a doubt again for next Wednesday against Schalke [in the UEFA Champions League] because of an accumulation of matches, but nobody can stop him.
"I tried to rest him, I tried to be sure, to be 100 per cent sure, but he goes on. He is a fantastic character. If the injury is a clear injury of course he will not play, but when the doubt is there and he has not the best feelings, but he feels he can play,"
