Spain striker Costa, who joined in the close season for 32 million pounds from Atletico Madrid, scored in Chelsea's opening Premier League victories over Burnley and Leicester City before picking up a muscle injury in training this week.
"We are trying everything for him to play tomorrow," Mourinho told reporters. "He didn't train for the last two days but today is the last day and we must make a decision to select him or not.
"He has to try a light training session to see if the reaction is positive. If it is we will take him to Everton to play or be on the bench, if the reaction is not positive today then obviously we don't select him."
If Costa fails to recover, Didier Drogba could lead the line against 10th-placed Everton as Torres continues to be linked with a transfer to Milan.
"What we have clear as a club is that we need three strikers this season," Mourinho said. "He (Torres) is one of them.
"I like him as a person, I like him as a player so that if he wants to leave it would be something he didn't say to me until this moment.
"If he wants to leave I believe it’s because he wants to try a new life, a new club, probably a new league," added Mourinho of out-of-favour Spain striker Torres.
HUMAN CLUB
"If he wants to leave, which I have not heard one single word about at this moment, I believe it is to try to be happier than he was in the last couple of years.
"This is a very human club in the way we approach these kinds of situations. If he comes to us in these last couple of days any possibility would be analysed from us as a club and we would make the best decision for him."
Mourinho said he had no plans to sign any more players for second-placed Chelsea ahead of Monday's transfer deadline.
"If that happens at the last hour of the market we are in trouble because at the moment we are doing nothing," said the Portuguese in reference to a Torres move.
"Our belief for a long time is that the squad is closed. Our squad is not the perfect one because not a single squad is the perfect one but it's a squad we like.
"At this moment we are ready for the market to close and for us to start Sept. 1 with the squad we have at this time."
(Editing by Tony Jimenez)
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